THE IMPACT OF
SAMPLING DENSITY ON GLACIER MASS BALANCE DETERMINATION
Mauri S. Pelto,
Dept. of Env. Science, Nichols College, Dudley, MA 01571 peltoms@nichols.edu
Summary
How many measurements are necessary to accurately assess the mass balance of a glacier? To identify the impact of sampling density on
determination of a
glacier’s annual mass balance, the North Cascade Glacier Climate Project
utilized a varying density of measurements to
determine annual mass balance on Columbia Glacier, Washington and Lemon Creek
Glacier, Alaska. Mass balance was
determined solely from field measurements.
The density of the mass balance networks ranged from 1 to 375 points/km^{2}.
The lesser density networks were subsamples of the highest measurement density
network. The
highest density network is probably the highest measurement density ever used in
mass balance observations. The point simply to see if an absurdly high
density helped improve accuracy. The results on both
glaciers indicate significant improvement in accuracy resulting from increasing
the total number of measurements from 1 to 4 points/km^{2} on Lemon
Creek Glacier and 12 to 46 points/km^{2} on Columbia Glacier.
There was no significant improvement in accuracy on the smaller Columbia
Glacier for utilizing more than 46 points/km^{2}.
On Lemon Creek Glacier there was little improvement in mass balance
assessment for a network greater than 4 points/km^{2}.
On both glaciers this represented a network of 40 measurement sites. The annual mass balance of a glacier is the most sensitive climatic measure of a glacier (IPCC, 1996). Annual mass balance is typically assessed from a sparse network (0.550 points/km^{2 }) of sample locations that are not uniformly distributed across the glacier (Pelto, 1996; Fountain and Vecchia, 1999). The main source of error in mass balance measurement programs arises from the nonrepresentativeness of this sparse measurement network from which the whole glacier estimate is determined (Cogley, 1996; Paterson, 1994).


^{ }
Table 2.
The annual balance in meters of water equivalent determined from field
measurements networks of varying number of measurement sites on Columbia
Glacier. The fewer the number of
measurements the more negative the annual balance calculated.

The Full Report which is published in Hydrologic Processes is below
Introduction:
Ideally, a mass balance measurement network is scattered uniformly over
the entire glacier with a density of measurements sufficient for statistical
testing of the results. Logistically,
measurements are only made at a limited number of points and some areas of
glaciers are too crevassed or steep to measure. Consequently, the resulting sparse network generates the
question: how many points is enough and how well do the measurement points
represent the area around them?
The typical density and total number of measurements currently used in
annual mass balance measurement is indicated in Table 1.
Measurement densities are usually below 10 points/km^{2}. Hence,
each point is assumed to accurately represent an area of 100,000 m^{2}.
Mean densities are higher in the accumulation zone (16 points/km^{2}),
than in the ablation zone (5 points/km^{2}). The North Cascade Glacier Climate Project (NCGCP), utilizes
the highest density of measurements 240 points/km^{2 }in the
accumulation zone and 10 points/km^{2} in the ablation zone.
Determining the most efficient sampling pattern and identifying the overall accuracy of the sampling network is key to assessing error in annual mass balance measurement. Llboutry (1974) and Cogley et al (1996 and 1999) and Fountain and Vecchia (1999) have approached this problem from a statistical standpoint and found that the number of measurement points can be fairly low 510 points/km^{2}, but that the overall pattern of mass balance must be known. Fountain and Vecchia (1999) found that five to ten measurement sites were sufficient to determine the mass balance of small glaciers. In this study, we approach the issue of errors resulting from measurements networks of varying densities from a purely field measurement perspective. Cogley (1999) pointed out that with a measurement network spaced at 50100 m apart the largest source of uncertainty is the error in actual point mass balance measurement (>0.05m), and sampling error is negligible. Cogley (1999) referred to the use of this density of measurements to eliminate all but measurement error, as reductio ad absurdum.
This technique is precisely what we have used on Columbia Glacier in the
North Cascades, Washington, and Lemon Creek Glacier Juneau Icefield, Alaska.
Both glaciers have a long annual mass balance record (Pelto, 1996; Miller
and Pelto, 1999). We compared the mass balance results from a dense network of
measurements with variously sparse networks, to determine the error resulting
from using increasingly sparse networks. The
sparse networks used are each subsamples of the larger network. Each network of points was chosen to provide the most even
distribution possible of measurements across each glacier, given the known mass
balance pattern.
GLACIER
CHARACTERISTICS
Columbia Glacier
Columbia Glacier is a south facing cirque glacier with a comparatively
low slope for a small alpine glacier (0.15).
The glacier has the lowest mean elevation (1600 m) of any glacier over
0.5 km^{2} in the North Cascades. In
1999 Columbia Glacier had an area of 0.87 km^{2}.
This low mean elevation, despite its southern exposure, is due to the
tremendous avalanching off of the 800 mhigh cirque walls on the east and west
sides of the glacier and the radiational shading the cirque walls provide
(Figure 1) (Pelto,1996). The
mean annual balance of Columbia Glacier has been measured by the NCGCP since
1984, using 169 point measurements each year (Figure 2). The mean annual balance of Columbia Glacier from
19841998 is –0.44 m/a, 6.55 m for the entire period (Figure 3) (Pelto,
1996). This is a substantial loss
for a glacier that averages less than 75 m in thickness.
The resultant glacier thinning, particularly pronounced near the
terminus, has caused extensive glacier retreat. The glacier has retreated
continuously during this century, 85 m since 1979.
Lemon Creek Glacier
In 1998, Lemon Creek Glacier was 5.6 km long and had an area of 11.8 km^{2
}(Figure 4) (Marcus et al., 1995).
From the head of the glacier at 1300 m to the mean Equilibrium Line
Altitude (ELA) at an elevation of 10501100 m
the glacier flows northward. In
the ablation zone the glacier turns westward terminating at 600 m.
The glacier has four distinct topographic sections: 1) Steep peripheral
northern and western margins draining into the main valley portion of the
glacier; 2) A low slope ( 4^{0}) upper accumulation zone from 1220 m to
1050 m; 3) A steeper section (6^{0})
in the ablation zone as the glacier turns west from 1050850 m;
4) An icefall (18^{0}) leading to the twofingered terminus at
600 m.
We determine annual balance on the Lemon Creek Glacier from a network of 830 points (Miller and Pelto, 1999). The Lemon Creek Glacier annual balance record indicates that from 19571976 mass balance was –0.23 m/a and thinning was modest on the upper reaches of the glacier (Miller and Pelto, 1999). Despite a higher mean elevation and a higher terminus elevation due to glacier retreat, mean annual balance has been increasingly negative since 1977, averaging 0.78 m/a. The record is particularly negative since 1990, 1.04 m/a (Miller and Pelto, 1999). This negative mass balance has fueled a terminal retreat of 800 m during the 19531998 period.
FIELD MEASUREMENT
METHODS
On Columbia Glacier in the North Cascades, Washington and Lemon Creek
Glacier Juneau Icefield, Alaska, we determined annual mass balance from
measurement networks of varying density. The
lowest density network was 1 point/km^{2} on Lemon Creek Glacier and 10
points/km^{2}on Columbia Glacier>
The highest density of measurements was 30 points/km^{2 }on Lemon
Creek Glacier and 375 points/km^{2 }on Columbia Glacier.
Each network is spatially fixed with respect to the adjacent bedrock
edges of the glacier and using differential GPS where necessary.
Each measurement transect on Columbia Glacier begins and ends at a fixed
location at the edge of the glacier. The
distance between measurement sites is measured, thus deviations in measurement
location are less than 15 m. On
Lemon Creek Glacier the deviations in measurement points was up to 50 m, the
accuracy of the GPS units at that time.
Mass balance is measured at the same point, using the same methods at
the same time of the year on each glacier.
On Columbia Glacier the measurements were completed on August 1 or 2 each
year from 19841998. On Lemon Creek
Glacier measurements were completed in July of 1984 and 1998.
The resultant mass balance reported here is not the actual annual balance
reported for each glacier and determined at the end of the hydrologic year
(October 1), but the specific mass balance of that date.
We used these dates because this is the time period when we have the
available resources to complete the dense measurement network.
Accumulation Zone
In assessing the
mass balance in the accumulation zone of Canadian, Norwegian, Swiss and United
States glaciers the average density of measurements is 16 points/km^{2 }(Pelto,
1996). On Columbia Glacier,
the typical density used in the mass balance measurements is 180 points/km^{2}.
On Lemon Creek Glacier, the density ranges from 14 points/km^{2}
(Miller and Pelto, 1999). In this
study the dense network on Columbia Glacier is 360 points/km^{2 }and on
Lemon Creek Glacier 100 points/km^{2}.
The mass balance measurement network covers a glacier's entire
accumulation zone with a consistent distribution of measurements (Figure 2 and
3).
Measurement of snow accumulation in the accumulation area was
accomplished using probing and crevasse stratigraphy.
Probing has proved both successful and easy to use in most temperate and
subpolar climate settings (Østrem and Brugman, 1991).
In the North Cascades and Juneau Icefield, all summers were notably warm,
resulting in a 25 cm thick band of continuous, readily identifiable dirtyfirn
that resists penetration.
Since North Cascade glaciers rarely have ice lenses, probing is an
accurate method of measuring accumulation layer thickness. The probe is driven
through the snowpack until the previous ablation surface is reached.
On the Juneau Icefield, ice lenses are more common but are discontinuous
and, thus, repeat measurement are often required to verify that the previous
annual layer has been reached.
Crevasse stratigraphic measurements were conducted only in
verticallywalled crevasses with distinguishable annual layer dirt bands.
Most of the vertically walled crevasses also tend to be less than 1 m
across.
The accuracy of crevasse stratigraphy and probing measurements are
crosschecked at a minimum of 25% of the measurement sites by probing between
crevasses. Occasional errors revealed by this crosschecking include ice
lenses that do not represent the annual layer in the case of probing, or in
crevasses which do not yield representative accumulation depth in the case of
crevasse stratigraphy.
The standard deviation in snow depth obtained in crosschecking and
duplicate measurements are smallest for crevasse stratigraphy, +0.02 m,
and +0.03 m for probing. The
narrow range of deviation in verticallywalled crevasses indicates that they do
yield consistent and representative accumulation depths late in the summer.
This is expected given the two dimensional view of crevasse stratigraphy
versus a single dimension in snowpits and probing (Pelto, 1997).
In ice sheet areas distant from a dust source this maybe difficult, but
on alpine glaciers mountaineers and glaciologists have long noticed the
ubiquitous nature of these layers (Post and LaChapelle, 1962).
In the North Cascades and Olympics, Washington, at the end of the summer
snowpack density of the most recent winter’s retained accumulation is
remarkably consistent (Pelto, 1996; Krimmel, 1998).
NCGCP completed more than 100 snowpits from 1984 to 1986 indicating that,
the range in mean accumulationlayer density for a single glacier was 0.590.63
Mg/m ^{3}. Of equal importance was that the range of density variation
is of the same order as the density measurement error, determined through repeat
measurements. Thus, density
measurements are no longer completed during crevasse stratigraphy or probing.
As is the case on South Cascasde Glacier (Krimmel, 1998) the mean density
used in our calculations of mass balance is 0.60 Mg/m^{3}.
NCGCP routinely measured the snow density using a SIPRE corer at several
location on each glacier each year, but has, to this date, found no deviation
from the above noted range. Snowpack
density in April and May measurements show a significant range in density, which
changes with time and must be considered in winter balance measurements.
Figure 2.
Mass balance map of Columbia Glacier.
Ablation Measurement
In the ablation zone, wooden stakes were emplaced in a sequence from
areas that lose their snowcover early in the summer to those that lose it late
in the summer and not at all. Ablation
stakes were white wooden poles, 3.3 m long.
This length was chosen as longer stakes were too cumbersome to transport
and emplace, and shorter stakes tend to melt out.
Ablation measurements were made at a minimum of six stakes on each
glacier. Measurements are made in late July and early August on
Columbia Glacier, recording the ablation during the first three months of the
ablation season, for water resource assessment purposes and redrilling of the
stakes when necessary. Ablation
measurements were repeated in late September at the designated conclusion of the
hydrologic year to determine total annual ablation.
On Lemon Creek Glacier, ablation measurements are completed each year in
July.
In this study the observed ablation in July on Lemon Creek Glacier
represents ablation since the previous July.
On Columbia Glacier the observed ablation in early August reflects the
ablation since the redrilling in early August of the previous summer.
RESULTS
We had the advantage of already understanding the overall mass balance
pattern of each glacier in selecting measurement networks that would provide the
most representative coverage for the glacier given the total number of
measurements in each sample (Pelto, 1996; Miller and Pelto, 1999).
Each measurement was assumed to represent the glacier area surrounding
that site. Each measurement
location for 10, 20, 40 and 80 measurement point networks was specifically
selected as the best representative of the average mass balance of the
surrounding region. The decision
was based on the existing detailed mass balance maps for each glacier.
We calculated the mass balance for each measurement network simply from
the mean of all the observations, without biasing the results according to the
representativeness of the specific sites.
On Columbia Glacier, we used a measurement network with a maximum
density of 375 points/ km^{2}, and a maximum spacing between points of
90 m and a mean spacing of 45 m. Annual
mass balance (19841998) was typically determined on Columbia Glacier from a
measurement network with a spacing of 187 points/ km^{2 }(Pelto, 1996),
and a mean spacing of 50 m.
On Columbia Glacier, using
12 points/km^{2 }(10 measurement points) yielded an error of –0.15
m/a, ranging from 0.07 m/a to –0.24 m/a.
For a network of 23 points/km^{2} (20 points), a consistent error
of –0.05 to –0.10 m/a resulted (Table 2). This measurement density provided an adequate measurement
network to determine annual mass balance with an error of 0.10 m/a.
The error resulting from the use of 23 points/km^{2} was
significant versus using either 46388 points/ km^{2} ( 40338
measurement points). However, the
consistency of the error for each year indicated by the parallel nature of the
annual balance trendlines for the varying point networks suggests even greater
accuracy was possible if the overall glacier balance distribution has been
determined at some time using a denser measurement network (Figure 5).
There was no significant change in annual mass balance for measurement
densities of 46100 points/ km^{2} (4084 points) compared to 23
points/km^{2 }(20 points) (Figure 5).
There was a small consistent change in mass balance when either 194
points/ km^{2 }or 388 points/ km^{2} (169338 measurment points)
are utilized, in comparison to the smaller measurement densities.
The difference in calculated annual balance ranged from –0.06—0.10
m/a. The lower measurement
densities consistently underestimated annual balance.
There is no significant difference between the mass balance observed at
169 versus 338 locations (Figure 6).
Figure 5.
Variation in measured annual balance on Columbia Glacier for each year,
19881998 depending on the number of mass balance measurement points used.
On Lemon Creek Glacier we used a measurement network with a maximum
density of 30 points/km^{2}.
The mass balance determined from a density of 1 to 2 points/km^{2 }(10
and 20 measurement sites) was significantly in error, unlike on Columbia Glacier
this error is not consistently negative, overestimating mass balance in 1984 and
underestimating mass balance in 1998 (Figure 6).
A measurement network of 1 point/ km^{2 }yielded an error of +0.15
m/a, ranging from 0.07m/a to –0.24 m/a.
Using a network of 2 points/km^{2} yielded an error of + 0.10
m/a in annual balance for a measurement network of greater than 2 points/ km^{2}. The mass balance determined from a network of 4 to 32
points/km^{2 }(40 to 320 measurement sites) yielded no significant
difference in observed annual balance. Thus,
on Lemon Creek Glacier, a density of 4 points/km^{2 }was adequate for
annual mass balance determination.
The variation from mass
balance between any two adjacent sites on Lemon Creek Glacier was low, a mean of
+ 0.07 m compared to that of + 0.35 m at Columbia Glacier.
This greater variation, despite the fact that the mean spacing of the
sites was 50 m on Columbia Glacier and 175 m on Lemon Creek Glacier. Thus, the measurement density necessary to yield reasonably
accurate mass balance values was lower for Lemon Creek Glacier.
The sheer size of the glacier caused the total required measurements to
be similar to achieve reasonable accuracy.
This was an expected result given that the majority of the Lemon Creek
Glacier shares much more homogenous topographic characteristics compared to
Columbia Glacier.
In order to achieve optimal accuracy, it is apparent that multiple
measurements are needed in each specific mass balance zone of the glacier.
If a glacier has large homogenous areas this reduces the measurement
density (Lemon Creek Glacier), if it has many small unique mass balance zones a
higher measurement density is required (Columbia Glacier).
CONCLUSIONS
To ascertain the annual balance of a glacier from a sparse network of
observations is optimized by detailed mapping of mass balance across the glacier
determined from a highdensity measurement network during several years.
Given that this has been accomplished on a small alpine glacier such as
the Columbia Glacier, a measurement density of 46 points/km^{2} (40
points) yielded accurate results. On
the larger Lemon Creek Glacier the measurement density needed to achieve
reasonable accuracy was 4 points/km^{2 }(40 points).
In both cases the total number of measurements necessary to achieve
consistent accuracy within +0.10 was 40 points. Statistical tests can be applied to compensate for lower
measurement densities, however, this always entails assumptions.
The aim of this study was to illustrate the minimum number of
measurements needed to determine annual mass balance accurately from field
measurements alone. The
results confirm Fountain and Vecchia (1999) conclusion that the number of
measurements necessary to determine mass balance on small alpine glaciers is
scale invariant, in this case that 40 points satisfactorily minimized errors on
both glaciers.
Glacier 
Ablation 
Area 
Accumulation 
Area 
Source 

Sites 
Density 
Sites 
Density 

Limmern 
12 
8 
17 
2 
A 
Silveretta 
4 
4 
4 
2 
A 
Greis 
5 
2 
5 
2 
A 
Place 
30 
11 
34 
20 
C 
Gulkana 
2 
5 
3 
3 
UA 
South Cascade 
5 
5 
5 
5 
UW 
Wolverine 
5 
1 
105 
6 
UW 
Alfotbreen 
5 
4 
126 
35 
N 
Austre Memurubre REmEMURUBREMemurubre 
8 
3 
316 
52 
N 
Grasubreen 
9 
8 
110 
40 
N 
Hellstugubreen 
13 
7 
125 
25 
N 
Nigardsbreen 
10 
4 
237 
5 
N 
Vestre Memurubre 
6 
4 
88 
10 
N 
Columbia 
3 
10 
165 
250 
P 
Daniels 
4 
12 
115 
280 
P 
Foss 
3 
15 
110 
240 
P 
Lower Curtis 
3 
10 
185 
280 
P 
Lynch 
3 
10 
125 
250 
P 
Rainbow 
3 
6 
200 
180 
P 
Table 1.
The number of measurement sites used and their density in km2
in mass balance studies on selected glaciers: In Switzerland (A)(Herren,
Hoelze, and Maisch, 1999), by the Canadian Inland Water Directorate (C)(Young
and Ommanney, 1984) by the United States Geological Survey (UW)(Krimmel: 1998) (UA)(March
and Trabant, 1995), by the Norges VassdragsElektrissen (N) (Østrem et al.
1980), and by the North Cascade Glacier Climate Project (P)(Pelto, 1996).
^{ }
Year 
10 points 
20 points 
40 points 
84 points 
169 points 
338 points 
1988 
0.46 m 
0.46 m 
0.51 m 
0.51 m 
0.58 m 

1989 
0.39 
0.4 
0.42 
0.41 
0.48 

1990 
0.41 
0.42 
0.44 
0.43 
0.5 

1991 
0.84 
0.84 
0.86 
0.85 
0.91 

1992 
0.28 
0.13 
0.11 
0.13 
0.04 

1993 
0.08 
0.01 
0.01 
0.01 
0.07 

1994 
0.06 
0 
0.02 
0.01 
0.08 

1995 
0.08 
0.13 
0.17 
0.14 
0.21 

1996 
0.05 
0.09 
0.12 
0.1 
0.17 
0.19 m 
1997 
0.77 
0.81 
0.84 
0.83 
0.92 
0.91 
1998 
0.23 
0.1 
0.09 
0.11 
0.01 
0.01 
Table 2.
The annual balance in meters of water equivalent determined from field
measurements networks of varying number of measurement sites on Columbia
Glacier. The fewer the number of
measurements the more negative the annual balance calculated.
Year 10 points 20 points 40 points 160 points 320 points 1984 0.38
m 0.32
m 0.23
m 0.24
m 0.24
m 1998 1.31 m 1.24 m 1.18 m 1.16 m 1.15 m
Table 3.
The observed annual balance on Lemon Creek Glacier determined from field
measurements of varying density in meters of water equivalent.
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