Effect of Ice on Mannings Roughness Coefficient in an Arctic River

1
Effect of Ice on Mannings Roughness Coefficient
in an Arctic River Jeffrey A. Oatley1, Larry D.
Hinzman1, Douglas L. Kane1, James P. McNamara2
1 Water and Environmental Research Center,
University of Alaska-Fairbanks, Fairbanks, AK
99775 2Department of Geosciences, Boise State
University, Boise, ID 83725
Abstract Due to the long, cold winters and
extensive permafrost conditions in the Arctic,
the smaller streams and the headwater reaches of
the larger rivers of this region typically freeze
solid to the bottom. Over the winter, the
channel also fills with aufeis that in some
places spills over into the adjacent floodplain.
During the snowmelt runoff event, the rivers are
still frozen and the runoff occurs over the
accumulated aufeis and channel ice. The runoff
process erodes the ice and over a one-to-four
week period removes the ice from the channel.
During the snowmelt period of 2002 the discharge,
channel cross section, and water surface slope
were monitored on the Upper Kuparuk River, in the
Alaskan Arctic, to determine how the Mannings
roughness coefficient, n, varied during this
dynamic event. At the onset of runoff on May
20th, while the ice was still fresh and hard, the
calculated roughness value of 0.025 was similar
to that of a sand bed stream. As the ice began
to erode and large blocks of ice broke free and
became entrained in the flow, the roughness value
increased to as high as 0.051. This maximum
roughness value corresponded in time with the
peak discharge value on May 24th. As the
discharge dropped, considerable ice still
remained in the channel, with less entrained in
the flow, and the roughness value decreased and
stayed near 0.040. On June 14th the ice-free
Mannings roughness value was calculated to be
0.050.
Study Site   The study was performed in the
Upper Kuparuk River, which is located in the
Alaskan Arctic. This river flows North from the
Brooks Range, across the North Slope of Alaska,
and into the Arctic Ocean. The Study location is
shown in Figure 1.   The study site was
located in the foothills of the Brooks Range
approximately 15 kilometers downstream from the
channel initialization. At this location, the
Figure 1. Study Location river drains an area
of 146 square kilometers. In the ice-free
periods the channel has a pool-riffle
morphology with a reach average slope of 0.009.
The bed material is primarily cobbles with many
boulders located throughout the reach.   A
fixed cable across the channel at the study site
facilitates stream gauging during high flow
periods. All measurements for this study were
made at this cross-section. The ice-free local
slope of this section is approximately 0.003.  
Figure 2. Summary of study results
Results   Figure 2 shows the measured
discharge, measured channel slope, and calculated
Mannings roughness, n, as these values
varied through the snowmelt period of 2002.
Unlike typical snowmelt periods, this
year as the hydrograph entered the recession
period more than a meter of ice remained
in the channel and it was not possible to
continue the measurements until the
channel was ice-free. A final,
ice-free, data point was taken on June 14th, two
weeks after the last data point with ice
in the channel.   As Figure 2
illustrates, break-up is a very dynamic period in
rivers of the arctic, with discharge, chann
el slope, and Mannings roughness coefficient all
changing rapidly. The plot has four
distinct phases indentified. These
phases are described below with a
corresponding photograph of the river
condition shown in Figure 3.
Phase 1 The
onset of runoff The initial Mannings
roughness value was calculated to be 0.025 on May
20th. This value corresponds to clean,
slush-free flow, over hard ice. Under these
conditions the flow quickly etched a dune-ripple
pattern in the ice. This dune-ripple pattern is
shown in photograph 1 of Figure 3. The
calculated Mannings roughness value of 0.025 is
similar to that of a dune-ripple sand bed
channel. Phase 2 Peak discharge   As the
flow continued to increase and erode the ice, the
ice became very porous and large sections
separated from the bottom leaving a non-uniform
bed surface and increasing the roughness value.
The discharge, as well as the roughness value
peaked on May 24th. At this time significant
numbers of large ice blocks were entrained in the
flow and becoming grounded in and near the study
cross section. This condition yielded a
roughness value of 0.051. Photograph 2 of
Figure 3 shows a photograph of the channel
condition at this time. Phase 3 Snowmelt
recession In the days following the peak
discharge the flow entered the recession phase.
In a typical year the channel is nearly ice-free
as the flow reaches this condition. In 2002
there was still 100 coverage of ice, although
the frequency and size of ice blocks in the flow
had decreased significantly and the Mannings
roughness value was near 0.040. Under nominal
conditions this scenario would likely have
continued until the channel was free of ice.
However, on May 28th the temperature dropped and
frazil ice and some surface ice returned to the
channel causing the roughness value to increase
to 0.050 on May 28th, before dropping back to
0.040 on May 30th. Photograph 3 of Figure 3
shows the conditions on May 29th when frazil ice
had caused an increase in the calculated
roughness value. Phase 4 Ice free
channel The ice-free roughness value for the
cobble and boulder channel was calculated to be
0.050 on June 14th. This condition is shown in
photograph 4 of Figure 3.   Figure 3. The
following sequence of photographs show the
channel condition at the different phases of the
break-up period.
2
4
Ice Free
3
1
Methods   Mannings equation is written
as Q (AR2/3S1/2)/n   Where Q
discharge (m3/s) A channel cross-sectional
area (m2) R hydraulic radius (m) S
channel slope (m/m) n Mannings roughness
coefficient   This relationship can be solved for
n as n (AR2/3S1/2)/Q   For this study
the discharge (Q), channel slope (S), and channel
cross-sectional area (A) were measured once a day
from the onset of the runoff period through the
recession of the snowmelt runoff. Hydraulic
radius (R) was calculated from the channel
cross-section data. Additional measurements were
made later in the summer to compare the ice-free
roughness coefficient with those obtained during
the spring break-up period.   The discharge was
measured using a Montadoro-Whitney electronic
current velocity meter. The channel
cross-sectional area and hydraulic radius data
were obtained in conjunction with the discharge
information.   The water surface slope was
measured, with each discharge measurement, using
a Leica Digital Level. The channel slope was
measured from a distance 12 meters (40 feet)
upstream of the cross-section to 12 meters
downstream of the cross-section. Measurements
were made every three meters.   The survey data
was then curve fit with a linear function and the
slope of that function was assumed to be the
water surface slope in the roughness
calculations.
Phase 2
Phase 4
Phase 1
Phase 3
Conclusions The purpose of this study was to
investigate the variation of the Mannings
roughness coefficient in an arctic river that
freezes solid during the winter and then melts
and erodes from the top surface downward during
spring break-up. There are several variables
that affect the timing and duration of the
break-up event including ice thickness, snow pack
water content, and ambient temperature. These
variables likely effect the variation of the
Mannings roughness value as well.
  Certainly the initial Mannings roughness
value does not vary much from one year to the
next. However, the peak value may vary
significantly depending on frequency and size of
the block ice that typically corresponds in time
with the peak discharge. 2002 was a year that
saw fairly extreme block ice in both size and
frequency. This condition likely resulted in a
higher-than-average roughness value during the
peak discharge phase of break-up.   Unlike rivers
that contain surface ice which increases the
Mannings roughness coefficient, in rivers that
freeze solid the ice presence reduces the
Mannings roughness coefficient of the river
during the snowmelt runoff period.
Information Contact Jeff Oatley WERC,
University of Alaska-Fairbanks, 525 Duckering
Building, Fairbanks, AK 99775-5860 907.474.2758 ft
jao_at_uaf.edu
Acknowledgements Funding for this project
provided by the USGS State Water Institute
Program and the NSF Office of Polar Programs,
Arctic System Science Program (OPP-9814984).