MASS BALANCE, METEOROLOGICAL, ICE MOTION,

SURFACE ALTITUDE, AND RUNOFF DATA AT GULKANA

GLACIER, ALASKA, 1992 BALANCE YEAR

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 95- 4277
Cover - Gulkana Glacier and basin, August 25, 1987, photograph #87R3-218 by Bob

Krimmel.
MASS BALANCE, METEOROLOGICAL, ICE MOTION, SURFACE

ALTITUDE, AND RUNOFF DATA AT GULKANA GLACIER,

ALASKA, 1992 BALANCE YEAR

by Rod S. March and Dennis C. Trabant

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 95-4277

Fairbanks, Alaska

1996
U. S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary

GEOLOGICAL SURVEY

Gordon P. Eaton, Director

For additional information write to: Copies of this report can be

purchased from:

District Chief U.S. Geological Survey

U.S. Geological Survey Earth Science Information Center

4320 University Drive, Suite 201 Open-File Reports Section

Anchorage, AK 99508-4664 Box 25286, MS 517

Denver Federal Center

Denver, CO 80225
iii

CONTENTS

Page

Abstract ..............................................................................................................................1

Introduction..........................................................................................................................1

Description and Climate.............................................................................................3

Measurement System and Terminology.....................................................................4

1992 Data Collection ...........................................................................................................8

Field Visits .................................................................................................................8

Recorded Variables ....................................................................................................9

Air temperature.......................................................................................................9

Precipitation catch ................................................................................................11

Runoff...................................................................................................................11

Photography..............................................................................................................12

1992 Mass Balance Evaluation..........................................................................................14

Mass Balance Measurement Errors..........................................................................14

Balance at Specific Sites ..........................................................................................14

Area-Averaged Balances..........................................................................................15

Weather in 1991-1992..............................................................................................23

Measured and Maximum Winter Snow Balances....................................................23

Net Balance ..............................................................................................................23

Summer Balance ......................................................................................................24

Annual Mass Balance...............................................................................................24

Accumulation Area Ratio and Equilibrium Line Altitude .......................................25

Ice Motion Measurement and Errors..................................................................................25

Glacier Surface Altitude Measurement and Errors............................................................27

References Cited ................................................................................................................31

ILLUSTRATIONS

Page

Figure1. Map of the Gulkana Glacier basin area, Alaska ....................................................4

2-9. Graphs showing:

2. Area-altitude distribution of Gulkana Glacier and west branch of Gulkana

Glacier in 1992...................................................................................................6

3. Time distribution of 1992 index-site mass balances......................................7

4. Time distribution of glacier-averaged mass balance......................................8

5. Daily mean air temperature recorded at 1,480 meters altitude ....................10

6. Daily precipitation-gage catch recorded at 1,480 meters altitude................11

7. Daily runoff from Phelan Creek near Paxson..............................................13

8. Altitude distribution of mass balance for 1966............................................21

9. Altitude distribution of mass balance for 1967............................................22
iv

TABLES

Page

Table 1. Data collection summary .....................................................................................2

2. Area-altitude distribution.....................................................................................5

3. Daily mean air temperature................................................................................10

4. Daily precipitation-gage catch ...........................................................................12

5. Daily mean runoff..............................................................................................13

6. Index-site stake, snow depth, snow density, and snow temperature data..........16

7. Continuation of index-site stake data with firn depth, firn density, and ice data18

8. Continuation of index-site stake data with mass balance calculations ..............19

9. Mapped and weighted index-site balances for 1966 and 1967..........................20

10. Area-integrated winter, annual, and net balance quantities .............................24

11. Stake locations, stake lean corrections, and ice motion...................................26

12. Glacier surface and summer-surface altitude measurements and analysis at

index sites ...........................................................................................................29

13. Continuation of glacier surface and summer-surface altitude measurements

and analysis at index sites...................................................................................30

CONVERSION FACTORS, VERTICAL DATUM, AND SYMBOLS

Multiply by To obtain

millimeter (mm) 0.03937 inch

centimeter (cm) 0.3937 inch

meter (m) 3.281 foot

kilometer (km) 0.6214 mile

square kilometer (km2) 0.3861 square mile

kilogram (kg) 2.205 pound

kilograms per liter (kg/L) 62.43 pound per cubic foot

kilograms per cubic meter (kg/m3

) 0.06243 pound per cubic foot

meters per year (m/yr) 3.281 feet per year

grad 0.9 degrees

degree Celsius (°C) °F = 1.8 × °C + 32 degree Fahrenheit (°F)

Vertical Datum:

Altitudes are measured relative to the National Geodetic Vertical Datum of 1929 (NGVD of

1929) which is defined as follows: A geodetic datum, formerly called SEA LEVEL DATUM OF

1929, derived from a general adjustment of the first-order level nets of both the United States and

Canada. In the adjustment, sea levels from selected TIDE stations in both countries were held

fixed. The year indicates the time of the last general adjustment. This datum should not be

confused with MEAN SEA LEVEL. Altitudes are the same in both the local coordinate system

and the Universal Transverse Mercator system.

Symbols used in this report:
v

AAR accumulation area ratio

b ̄ area-averaged balance value

b' average stake height of the glacier surface within a 50-meter radius of the stake, in

meters

b0' initial average stake height of the glacier surface within a 50-meter radius of the stake, in

meters

b* stake height of surveyed point near b' on the stake, in meters

b** calculated stake height of the glacier surface directly above the stake bottom (i.e. as if

the stake were vertical), in meters

ba annual balance at site

b ̄ a area-averaged annual balance

ba(fi) annual firn and ice balance at site

b ̄ a(fi) area-averaged annual firn and ice balance

bn net balance at site

b ̄ n area-averaged net balance

b ̄ s area-averaged summer balance

b ̄ w area-averaged winter balance

b(f) firn balance at site

b(i) ice balance at site

b0(i) initial ice balance at site

b1(i) late ice balance at site

b(k) internal accumulation at site

b1(ls) final late snow balance at site

b ̄ 1(ls) area-averaged final late snow balance

b(s) snow balance at site

b0(s) initial snow balance at site

b ̄ 0(s) area-averaged initial snow balance

bm(s) measured winter snow balance at site

b ̄ m(s) area-averaged measured winter snow balance

bw(s) maximum winter snow balance at site

b ̄ w(s) area-averaged maximum winter snow balance

d(s) snow depth, in meters

d(nf) new firn depth, in meters

E UTM Easting

ELA equilibrium line altitude

Ht height of the stake upper target above the stake bottom as measured along the stake, in

meters

HY hydrologic year; interval between October 1 and the end of the following September

k horizontal scale factor between the UTM plane and sea level

 ̄ mean horizontal scale factor between the UTM plane and sea level k

mwe meters water equivalent

n sample number

ss1 first glacier summer surface down from the glacier surface (this is typically a bare ice

surface in the ablation zone and a firn surface in the accumulation zone)

ss2 second glacier summer surface down from the glacier surface (this is typically a firn

surface; multiple summer surfaces only occur in the accumulation zone of the

glacier)

Xg local sea-level coordinate of measurement stake at glacier surface, in meters

Xi horizontal coordinate of fixed index site

XL local sea-level coordinate, in meters
vi

Xs local sea-level coordinate of bottom of measurement stake, in meters

Xt local sea-level coordinate of stake upper target, a point on the stake 1.5-2.0 meters above

the glacier surface, in meters

Yg local sea-level coordinate of measurement stake at glacier surface, in meters

Yi horizontal coordinate of fixed index site

YL local sea-level coordinate, in meters

Ys local sea-level coordinate of bottom of measurement stake, in meters

Yt local sea-level coordinate of stake upper target, a point on the stake 1.5-2.0 meters above

the glacier surface, in meters

Z altitude, in meters

Zg altitude of measurement stake at glacier surface, in meters

Zi altitude of glacier surface at index site, in meters

Zs altitude of bottom of measurement stake, in meters

Zt altitude of stake upper target, a point on the stake 1.5-2.0 meters above the glacier

surface, in meters

dXYZ total three-dimensional displacement of the stake bottom between measurements

θ down-dip direction with zero east and positive counterclockwise

φ dip angle with zero horizontal and positive angles up
1

MASS BALANCE, METEOROLOGICAL, ICE MOTION, SURFACE

ALTITUDE, AND RUNOFF DATA AT GULKANA GLACIER,

ALASKA, 1992 BALANCE YEAR

by Rod S. March and Dennis C. Trabant

ABSTRACT

The 1992 measured winter snow, maximum winter snow, net, and annual balances in

the Gulkana Glacier basin were evaluated on the basis of meteorological, hydrological,

and glaciological data measured in the basin and are reported herein. Averaged over the

glacier, the measured winter snow balance was 0.97 meters on March 26, 1992; the

maximum winter snow balance was 1.05 meters on May 19, 1992; the net balance (from

September 8, 1991 to August 17, 1992) was -0.29 meters; and the annual balance

(October 1, 1991 to September 30, 1992) was -0.38 meters. Ice surface, motion, and

altitude changes measured at three index sites document seasonal changes in ice speed

and glacier thickness. Annual stream runoff was 1.24 meters averaged over the basin.

INTRODUCTION

The U.S. Geological Survey has a long-term program to monitor climate, glacier

motion, mass balance, and stream runoff to understand glacier-related hydrologic

processes for improving the quantitative prediction of water resources, glacier-related

hazards, and the consequences of global change. The approach has been to establish longterm mass balance monitoring programs at three widely spaced glacier basins in the

United States that clearly sample different climate-glacier-runoff regimes. Gulkana

Glacier is one of three long-term, high-quality mass balance monitoring sites operated by

the U.S. Geological Survey. The other monitoring sites are Wolverine Glacier in southcentral Alaska and South Cascade Glacier in Washington. This report contains the mass

balance, meteorological, ice motion, surface altitude, and basin runoff measurements

made in the Gulkana Glacier basin during 1992 (table 1) as part of the long-term

monitoring program.

Measurements began on Gulkana Glacier during the early 1960’s with the University

of Alaska Gulkana Glacier Project. For several years this project measured the energy

budget, mass balance, meteorology, foliation, flow, and glacier bottom topography (from

gravity anomalies) at Gulkana Glacier. In 1966, a continuing series of meteorology, snow

and ice balance, and runoff measurements was begun by the U.S. Geological Survey as

part of the United States contribution to the International Hydrologic Decade study of

mass balances on selected glaciers. Detailed results from 1966 and 1967 are reported by

Meier and others (1971) and Tangborn and others (1977), respectively. Measured winter

snow balance and annual balance from 1966-77 are reported by Meier and others (1980).
on summary, 1992 hydrologic year (the location of the stations are shown on figure 1)

 -, estimated record; •, occasional/discrete measurement]

1992 Hydrologic Year 1993 Hydrologic Year

urement 1991 Calendar Year 1992 Calendar Year 1993 Calendar Year

Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar.

low

ge Meas.

alance

 Motion Altitude

perature

ation

alance

 Motion Altitude

alance

 Motion Altitude

d

y
3

Balance studies were relatively intensive until the mid-1970’s, after which spatial

sampling was reduced to three index sites, but measurements were expanded to include

ice motion and surface altitude observations (for glacier volume change) in addition to the

balance, runoff, and meteorology observations previously being made. Since 1966, part of

the Gulkana data set (net balance, accumulation, ablation, accumulation area ratio (AAR),

and equilibrium line altitude (ELA)) has been published by the World Glacier Monitoring

Service (Kasser, 1967; Muller, 1977; Haeberli, 1985; Haeberli and Müller, 1988;

Haeberli and Hoelzle, 1993). Index-site glacier-surface and summer-surface altitudes,

measured winter balance, and net firn and ice balance from 1975 to 1983 are reported by

Mayo and Trabant (1986).

The Gulkana record is just approaching the general 30-year length-of-record criterion

(necessary to provide reasonable statistics) that is used in the selection of stations for

international exchange through the Global Telecommunications Service (GTS) for global

climate monitoring (Karl and others, 1989). Hence, the current record is only marginally

valuable for long-term analysis. Preliminary regional climate-glacier interpretive work

using the Gulkana data includes papers by Walters and Meier (1989) and by Letréguilly

and Reynaud (1989).

Description and Climate

Gulkana Glacier (fig. 1) (lat 63°16' N., long 145°25' W.) is a compound valley glacier

fed from several cirques on the south flank of the eastern Alaska Range. The glacier and

basin area-altitude distributions (table 2; fig. 2) were defined in 1967 above the runoff

gage at 1,125 m altitude. These values are used throughout this report. In 1967, the

31.6-km2 basin was 70 percent covered by perennial snow and ice. Gulkana Glacier is the

largest glacier in the basin covering 19.32 km2. The basin also contains Pegmatite Glacier

(fig. 1), three small, unnamed glaciers, and perennial snow and ice patches that had a total

area of 2.9 km2. The accumulation area of Gulkana Glacier is four adjacent cirques with

east, south, and west exposures reaching as high as 2,470 m altitude. The cirque glaciers

converge forming a south-flowing ablation area with a terminus lightly covered with

rock-debris (cover photo) at 1,160 m altitude. Contorted moraines suggest that Gulkana

Glacier has surged (see cover photo). However, no flow instabilities have been detected

since scientific investigation began in the early 1960's. Gulkana Glacier has been in

general recession since the culmination of its last advance around the turn of the century

(Péwé and Reger, 1983). The total recession since then has been about 3 km.

Phelan Creek drains the Gulkana Glacier basin and flows into the Delta River, which

is a tributary of the Tanana River, and finally into the Yukon River north of the Alaska

Range. In the past, Phelan Creek occasionally drained into Summit Lake at the head of

the Gulkana and Copper Rivers. The alternating drainage was diverted into the Yukon

River basin when the Richardson Highway was constructed in 1923.
4

Figure 1. Gulkana Glacier basin area, Alaska. (Contour interval is 100 m. Base map from

Tangborn and others, 1977.)

The mean ELA is near 1,735 m, which is consistent with a continental mountain

climate. The mean annual air temperature near the ELA is about -6°C, lapsed from the

recorder site using the wet adiabatic rate of -6.6°C per 1,000 meters. The mean annual air

temperature at the recorder site at 1,480 m altitude is about -4°C, and the average annual

precipitation-gage catch is about 1,160 mm. Daily mean temperatures range from a low of

-35°C to a high of 15°C. The average annual basin runoff for water years 1967-78 and

1989-92 is 1.89 m.

Measurement System and Terminology

Seasonal monitoring on Gulkana Glacier consists of three basic measurements:

surface mass balance, ice velocity, and surface altitude. These measurements are

repeatedly made at three fixed locations on Gulkana Glacier, referred to as the “index

sites.” Balance-motion stakes maintained near each index site support the long-term data

collection.
5

Table 2. Area-altitude distribution of Gulkana Glacier and Gulkana Glacier basin by

100-meter altitude intervals

[m, meters; km2, square kilometers]

Gulkana Glacier Gulkana

Sub-areas of glacier 

represented

by index sites:

Altitude Average Basin west branch Glacier Site A Site B Site D

interval altitude area area area 1373 1685 1837

(m) (m) (km2

) (km2) (km2) (km2) (km2) (km2)

1,161 - 1,200 1,180.5 0.84 0.12 0.12

1,200 - 1,300 1,250 1.48 0.52 0.52

1,300 - 1,400 1,350 1.92 1.20 1.20

1,400 - 1,500 1,450 2.68 1.56 1.56

1,500 - 1,600 1,550 2.44 1.36 0.39 0.97

1,600 - 1,700 1,650 3.68 0.43 2.12 2.12

1,700 - 1,800 1,750 4.00 0.44 2.04 1.24 0.80

1,800 - 1,900 1,850 4.28 0.91 2.72 2.72

1,900 - 2,000 1,950 4.32 1.31 2.92 2.92

2,000 - 2,100 2,050 2.72 0.96 2.28 2.28

2,100 - 2,200 2,150 1.92 0.78 1.44 1.44

2,200 - 2,300 2,250 1.04 0.37 0.80 0.80

2,300 - 2,400 2,350 0.24 0.06 0.20 0.20

2,400 - 2,473 2,436.5 0.04 0.00 0.04 0.04

Total area = 31.60 5.28 19.32 3.79 4.33 11.20

Average altitude = 1,748 1,965 1,797 1,393 1,656 1,988

Upper altitude limit of zone = 1,529 1,761 2,473

Lower altitude limit of zone = 1,161 1,529 1,761

Percent of total glacier area = 19.6% 22.4% 58.0%

The combined mass balance system of measurement and reporting terminology

(Mayo, Meier, and Tangborn, 1972) is adhered to in this report, with the addition of

internal accumulation (Trabant and Mayo, 1985). The combined mass balance system is

based on measurements relative to time-transgressive stratigraphic horizons (summer

surfaces) and evaluation of adjustment quantities for determining the fixed-date annual

balance. Both net (stratigraphic) and annual (fixed-date) balances are derived from field

measurements. The balance year used for the net mass balance is, in principle, the interval

between the minimum, glacier-wide mass balance in one year and the minimum, glacierwide mass balance the following year. Thus, the net balance would have a beginning and

ending date. In actuality, reported net balances are approximations to this ideal and do not

have a specific beginning and ending date most years because of the time transgressive

formation of the glacier summer surface. In this and most other mass balance work, net

balance is determined for each measurement location on the glacier as the difference

between successive balance minimums and then combined for the whole glacier as if the

balance minimum occurred synchronously over the whole glacier.
6

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500

ALTITUDE, IN METERS

AREA, IN SQUARE KILOMETERS

SITE A

SITE B

SITE D

WEATHER STATION

MEAN EQUILIBRIUM LINE

MEAN ALTITUDE

WEST BRANCH

Figure 2. Area-altitude distribution of Gulkana Glacier and west branch of Gulkana

Glacier in 1992. (Shown are altitudes of index sites, the weather station (air

temperature and precipitation gage), the mean equilibrium line altitude, and

mean glacier altitude.)

The hydrologic year (HY), which is the period used for the annual mass balance, is

the interval between October 1 and the end of the following September. It is designated

by the calendar year in which it ends. The hydrologic year coincides with the “water year”

used for publishing U.S. Geological Survey hydrologic data. The temporal relation of the

quantities defined and used for analyzing the index-site and glacier-averaged 1992 mass

balances are illustrated in figures 3 and 4.

All balance, precipitation, and runoff values are reported in meters of water

equivalent. All reported densities are relative densities; i.e. the decimal fraction of the

density of water. The density of water is assumed to be 1,000 kg/m3

 and the relative

density of glacier ice is assumed to be 0.9.

Balance-motion-stake and index-site-altitude locations are reported in local, metric

coordinates, with the positive Y-axis approximately true north. Altitude is in meters

above the National Geodetic Vertical Datum of 1929. Horizontal locations are defined in

a local sea-level-scale network that may be converted to Universal Transverse Mercator

(UTM) zone 6 coordinates in the North American Datum 1983 by:
7

UTM Easting = k

_

XL + 575,000 m (1)

UTM Northing = k

_

YL + 7,011,000 m. (2)

where XL and YL are local sea-level coordinates in meters and k

_

 is the mean horizontal

scale factor between the UTM plane and sea level.

- 3.0

- 2.5

- 2.0

- 1.5

- 1.0

- 0.5

0.0

0.5

1.0

1.5

2.0

MASS BALANCE, IN METERS WATER EQUIVALENT

 OLD FIRN OR ICE | SNOW

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP

Site A, 1370 m.

Site B, 1685 m.

Site D, 1840 m.

SNOW

OLD FIRN OR ICE

b m(s)

b w(s)

b n

b m(s)

b m(s)

New

Firn

late snow

late snow

late snow

Figure 3. Time distribution of 1992 index-site mass balances for Gulkana Glacier. (Solid

circles are measured values; open circles are estimated values. Seasonal

maximum balances occurred in mid-May. bm(s), measured winter snow balance

at site; bn, net balance at site; bw(s), maximum winter snow balance at site.)

The scale factor, k, at a point is a variable defined by:

k

E =

+  −



 





0 9996

100 500 000

100 000

.

sin ,

,

(3)

where E is the UTM Easting of the point and the trigonometric function is evaluated in

grad.
8

The mean scale factor used in equations 1 and 2 to convert between the local sea-level

system coordinates and UTM coordinates is the mean value of the nonlinear distribution

of scale factors between the local sea-level system origin and an observation point. E is

approximated by the sum of the UTM Easting of the local system origin (575,000 m) and

XL. The mean scale factor is estimated using Simpson’s 1/3 rule:

k

X X L L

=

+  −



 





+

+  − −



 





+

+  − −



 





























09996

6

1

100 500 000 575 000

100 000

4

100 500 000 575 000

100 000

1

100 500 000 575 000

100 000

.

sin , ,

, sin , , 1⁄2

, sin , ,,

(4)

Equation 4 is accurate within about 0.1 part per million of equations from U.S.

Departments of the Army and the Air Force (1941) and hence yields results accurate at

the centimeter level.

- 0.6

- 0.4

- 0.2

0.0

0.2

0.4

0.6

0.8

1.0

GLACIER-AVERAGED MASS BALANCE,

IN METERS WATER EQUIVALENT

b s o( )

OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP

b s m( )

b s bk bi m() ( ) () + +

b s m( ) b s w ( )

bn ba

Figure 4. Time distribution of glacier-averaged mass balance of Gulkana Glacier, 1992

hydrologic and balance years. (The initial balance, b ̄ 0(s), is the change in

balance between the balance minimum that defines the beginning of the balance

year and the beginning of the hydrologic year (1 October). The measured winter

snow balance, b ̄ m(s), is the snow above the previous summer surface measured

directly in the field near the time of the maximum snow balance, b ̄ w(s). Solid

circles are measured values; open circles are estimated values. Symbols with a

bar over them indicate the mean value over the whole glacier.)

1992 DATA COLLECTION

The temporal distribution of the data used to analyze the 1992 mass balance is shown

in table 1.
9

Field Visits

Six field visits to the Gulkana Glacier basin between early September 1991 and late

March 1993 (table 1) were used to collect the data necessary to evaluate the 1992 glacier

mass balance, motion, and surface altitudes and to service and calibrate recorders. Site

visits are made by foot, snowmachine, or helicopter depending on the conditions and

work to be done. Generally the trips are timed to define the mass balance maximums and

minimums, usually during a spring trip (March/April/May) and a late-summer/early-fall

trip (September/October) respectively. Sometimes for safety reasons, the fall trip is split

(table 1, fall 1991): one trip on foot to the lower glacier and recorders and a second trip

with a helicopter to measure the upper glacier (fall glacier travel is notoriously unsafe in

crevassed regions). An additional trip was made during July 1992 to measure mass

balance and glacier motion, and to resurvey glacier longitudinal profiles, cross profiles,

and control points for analysis of long-term glacier volume change and in preparation for

photogrammetric mapping. Measurements in March 1993 add redundancy to the

September and October 1992 measurements of the height of the 1992 summer surface on

stakes and allow for the regular assessment of errors in balance calculations based on

stake readings.

Recorded Variables

Data on air temperature, precipitation-gage catch, and stream runoff are recorded

continuously, although the runoff data typically become meaningless after Phelan Creek

freezes over in the early fall. The data sets are truncated to the hydrologic year. Periods of

good recorder data are shown in table 1.

AIR TEMPERATURE

Air temperature is recorded by an analog recorder at 1,480 m altitude on the eastern

ice-cored moraine of Gulkana Glacier (weather station, fig. 1). The air temperature

sensor, data reduction methodology, and data accuracy described for a similar gage at

Wolverine Glacier (Mayo, March, and Trabant, 1992; Kennedy, 1995) are applicable to

the Gulkana gage and data. Briefly, the sensor is a copper-finned, 20-x-300 mm, liquidfilled sensor designed for use in water. It has a slow response time in air that makes it

good for determining daily average temperature, but poor for daily maximum and

minimum temperatures. The sensor is housed in a small white shelter with slatted walls

and an open bottom, 1.5-2.0 m above the ground. Snow accumulation is minimal at the

site, so the height above the ground is not significantly reduced during the winter. A glass

thermometer with one- or two-tenths graduations is used several times a year to make

calibration measurements. The preliminary daily mean temperatures reported (fig. 5, table

3) have an accuracy of about ±1.0°C (Mayo, March, and Trabant, 1992; Kennedy, 1995).

Part of the 1992 record was lost because of recorder failure.
10

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep 

-30

-25

-20

-15

-10

-5

0

5

10

NO DATA 6/3/92 to 9/22/92

NO DATA

11/19/91 to 1/29/92

1991 1992

TEMPERATURE, IN °C

Figure 5. Daily mean air temperature recorded at 1,480 meters altitude in the

Gulkana Glacier basin.

Table 3. Daily mean air temperature from the recording gage at 1,480 meters altitude

[Values in degrees Celsius; Not Valid indicates monthly average temperature has more than 9 days missing;

—, daily value missing.]

1991 1992

Day Oct Nov Dec Jan Feb Mar Apr May June July Aug Sept

1 - 1.7 - 4.4 — — - 8.7 -17.2 - 7.5 - 4.7 3.2 — — —

2 - 1.6 - 3.8 — — -12.4 -26.6 -13.7 - 4.9 2.7 — — —

3 - 1.2 - 9.2 — — -11.3 -27.7 -14.8 - 9.8 — — — —

4 - 1.4 - 3.5 — — - 9.4 -26.1 -15.6 - 8.5 — — — —

5 - 3.1 - 4.0 — — - 8.2 -23.9 -13.6 - 7.3 — — — —

6 - 5.6 - 3.0 — — -12.3 -14.5 -10.1 - 8.8 — — — —

7 - 7.2 - 9.1 — — -12.5 - 8.1 -10.3 - 4.2 — — — —

8 - 7.0 -10.1 — — -12.6 - 4.1 - 9.1 - 5.4 — — — —

9 - 9.3 - 5.9 — — - 6.3 - 6.9 - 8.4 - 7.3 — — — —

10 - 8.0 - 6.2 — — -10.5 - 4.1 -11.8 -11.6 — — — —

11 - 7.4 - 8.5 — — -15.4 - 5.2 -18.5 - 5.6 — — — —

12 - 8.0 -13.5 — — -15.8 - 7.5 -17.0 - 4.9 — — — —

13 - 2.1 -18.2 — — -16.1 - 7.3 -14.3 - 3.8 — — — —

14 - 3.2 - 9.8 — — -19.4 - 9.4 - 6.6 - 3.8 — — — —

15 - 9.2 -11.9 — — -18.5 - 8.2 2.2 - 9.6 — — — —

16 -11.8 -11.5 — — -23.4 - 8.0 - 3.5 -12.6 — — — —

17 - 7.2 -10.9 — — -27.2 - 9.4 - 4.3 - 7.5 — — — —

18 - 5.2 - 7.2 — — -20.7 -10.4 - 5.7 - 4.7 — — — —

19 - 3.2 — — — -20.7 - 7.7 - 4.3 - 3.4 — — — —

20 -10.3 — — — -24.7 - 7.9 - 3.7 1.6 — — — —

21 -11.4 — — — -19.0 - 8.9 - 6.9 2.8 — — — —

22 - 9.6 — — — -18.6 -10.3 - 5.4 2.2 — — — —

23 - 8.7 — — — -12.4 - 9.4 - 3.7 4.7 — — — -12.1

24 - 8.3 — — — -11.1 - 8.1 - 5.4 5.8 — — — -12.6

25 - 9.4 — — — - 5.5 - 7.6 - 3.6 7.0 — — — -10.0

26 -10.7 — — — - 3.2 - 8.2 - 3.9 1.9 — — — -10.4

27 - 8.3 — — — - 2.9 -10.2 - 5.3 3.1 — — — - 5.6

28 -10.6 — — — -11.2 -12.5 - 5.4 3.9 — — — - 8.1

29 - 6.3 — — — -14.1 -13.6 - 4.4 3.4 — — — -12.4

30 - 6.2 — — - 9.0 -10.8 - 5.1 2.7 — — — - 7.6

31 - 7.0 — - 7.1 - 8.5 2.5 — —

Month

Average - 6.8 Not Valid Not Valid Not Valid -13.9 -11.2 - 8.0 - 2.8 Not Valid Not Valid Not Valid Not Valid

Annual Average Temperature = Not Valid
11

PRECIPITATION CATCH

Precipitation catch is recorded by an analog recorder at the air temperature site

(fig. 1). The gage, data reduction methodology, and data accuracy have been described for

a similar gage at Wolverine Glacier (Mayo, March, and Trabant, 1992; Kennedy, 1995).

Briefly, the gage consists of a steel storage tank that tapers to a conical orifice, 0.305 m in

diameter, 3 m above the ground. A modified Nipher shield (Warnick, 1953) is installed

around the orifice to improve the catch efficiency during windy conditions. The

preliminary daily precipitation catch (fig. 6, table 4) has an estimated accuracy of

±0.001 m and the cumulative gage catch for monthly and annual values is estimated to

have an accuracy of ±0.002 m (Mayo, March, and Trabant, 1992; Kennedy, 1995).

The complex relation between precipitation catch and true basin precipitation has not

been thoroughly analyzed at Gulkana. It is generally well known that gage catch

efficiency is reduced by strong winds, especially for snow precipitation. Worse, catch

efficiencies are not constant but vary with wind speed, direction, and the nature of the

precipitation. At Wolverine Glacier, which has a windier environment than Gulkana, the

gage-catch efficiency was found to be about 0.31 relative to the basin precipitation for a

10-year period (Mayo, March, and Trabant, 1992). From April 27, 1967 to September 30,

1967 the catch efficiency of the Gulkana gage was calculated at 0.52 (Tangborn and

others, 1977), though the wind shield has since been modified to what we believe is a

more efficient design. Despite the low catch efficiencies, precipitation catch is useful as a

precipitation indicator.

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep 

0

5

10

15

20

25

NO DATA 6/3/92 to 9/22/92 NO DATA

11/19/91 to 1/29/92

1991 1992

DAILY GAGE CATCH, IN MILLIMETERS

Figure 6. Daily precipitation-gage catch recorded at 1,480 meters altitude in the Gulkana

Glacier basin.

RUNOFF

The Phelan Creek stream-gaging station, USGS no. 15478040, is located at 1,125 m

altitude, about 1 km downstream from the present glacier terminus (fig. 1). The creek bed

is composed of typical ground moraine material, poorly sorted gravel and small boulders.

The channel is subject to frequent changes during high flows. The published discharge

record is rated as "poor" meaning that the records do not meet the criteria for a “fair”
12

Table 4. Daily precipitation-gage catch from the recording gage at 1,480 meters altitude

[Values in millimeters; Not Valid indicates monthly accumulated precipitation has more than 9 days missing;

— , daily value missing]

1991 1992

Day Oct Nov Dec Jan Feb Mar Apr May June July Aug Sept

1 90 — — 0 3 1 0 0— — —

2 1 0— — 2 5 2 0 8— — —

3 7 0— — 0 1 1 0— — — —

4 3 0— — 0 0 1 0— — — —

5 0 0— — 0 0 0 5— — — —

6 0 0— — 2 0 0 4— — — —

7 0 0— — 0 0 0 0— — — —

8 0 0 — — 37 1 0 15 — — — —

9 0 0— — 0 3 0 1— — — —

10 0 0 — — 0 0 0 2 — — — —

11 0 0 — — 4 3 4 0 — — — —

12 0 2 — — 0 2 1 4 — — — —

13 0 0 — — 0 0 0 12 — — — —

14 0 0 — — 1 3 0 0 — — — —

15 0 0 — — 0 1 0 5 — — — —

16 0 0 — — 0 2 0 3 — — — —

17 0 0 — — 0 1 0 0 — — — —

18 3 1 — — 0 3 0 0 — — — —

19 24 — — — 0 0 0 0 — — — —

20 5 — — — 0 0 0 0 — — — —

21 0 — — — 0 3 0 0 — — — —

22 0 — — — 0 3 0 0 — — — —

23 0 — — — 0 1 0 0 — — — 0

24 0 — — — 0 0 0 0 — — — 0

25 0 — — — 0 11 0 0 — — — 0

26 0 — — — 11 1 0 0 — — — 0

27 0 — — — 3 2 0 0 — — — 9

28 0 — — — 7 4 0 0 — — — 0

29 0 — — — 1 0 0 0 — — — 0

30 0 — — 144 0 0 0 — — — 0

31 0 — 0 0 0 — —

Month

Total 52 Not Valid Not Valid Not Valid 68 53 10 51 Not Valid Not Valid Not Valid Not Valid

Annual Total = Not Valid

rating which is defined as “about 95 percent of the daily discharges are within 15 percent

of the true value” (Kemnitz and others, 1993). This formal rating places no limit on the

possible error. It is estimated that the standard error of the measured daily discharge

values during the open-water season at Phelan Creek is about 8 percent (Richard

Kemnitz, U.S. Geological Survey, oral commun., 1995). No stage record was collected

during the winter when Phelan Creek freezes over. Discharge values are estimated for the

ice period on the basis of air temperature, precipitation, and winter discharge

measurements (November 8, 1991; February 6, 1992; and March 27, 1992). The 1992

daily mean discharge data (Kemnitz and others, 1993) were converted to runoff (fig. 7,

table 5) by dividing the discharge values by the basin area. The 1992 stream runoff from

the basin was 1.24 m.

Photography

Parts of the Gulkana Glacier basin were photographed from low altitude and the

ground with a hand-held 35-mm camera during the 1992 HY (table 1).
13

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep 

0

10

20

30

40

 Discharge Measurements

1991 1992

DAILY RUNOFF, IN MILLIMETERS

Figure 7. Daily runoff from Phelan Creek near Paxson (USGS stream-gaging station

no. 15478040) (Kemnitz and others, 1993).

Table 5. Daily mean runoff of the Gulkana Glacier basin calculated from the published

discharge of USGS stream-gaging station no. 15478040, Phelan Creek near Paxson, at

1,125 meters altitude, and the basin area (Kemnitz and others, 1993)

[Values in millimeters, averaged over the basin; () indicates value estimated (see text for explanation)]

1991 1992

Day Oct Nov Dec Jan Feb Mar Apr May June July Aug Sept Annual

1 1.9 ( 0.7) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.4) 29.5 8.7 1.7

2 1.9 ( 0.7) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.5) 33.3 8.4 1.6

3 1.8 ( 0.7) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.5) 37.6 5.4 1.5

4 ( 1.7) ( 0.7) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.6) 38.3 9.3 1.5

5 ( 1.5) ( 0.7) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.8) 32.9 12.8 1.4

6 ( 1.5) ( 0.6) ( 0.5) ( 0.4) 0.3 ( 0.2) ( 0.2) ( 0.2) ( 0.9) 27.6 14.1 1.4

7 ( 1.5) ( 0.6) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 1.1) 34.5 16.3 1.3

8 ( 1.4) 0.6 ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 1.5) 24.3 16.3 1.2

9 ( 1.3) ( 0.6) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 2.1) 27.2 9.1 1.1

10 ( 1.3) ( 0.6) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 3.4) 30.6 8.6 ( 1.1)

11 ( 1.2) ( 0.6) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 9.6) 28.7 6.7 ( 1.1)

12 ( 1.2) ( 0.6) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 11.0 31.1 5.7 ( 1.1)

13 ( 1.2) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 11.7 28.3 4.4 ( 1.1)

14 ( 1.2) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 11.9 23.5 3.8 ( 1.0)

15 ( 1.1) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 13.6 19.7 2.9 ( 1.0)

16 ( 1.1) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 13.0 21.4 2.7 ( 1.0)

17 ( 1.0) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 11.0 19.7 2.2 ( 1.0)

18 ( 1.0) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 8.7 20.7 2.4 ( 0.9)

19 ( 0.9) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 8.8 20.0 2.4 ( 0.9)

20 ( 0.9) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 9.8 24.1 2.4 ( 0.9)

21 ( 0.9) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 12.9 17.7 2.5 ( 0.9)

22 ( 0.9) ( 0.5) ( 0.4) ( 0.3) ( 0.3) ( 0.2) ( 0.2) ( 0.2) 13.4 13.6 3.6 ( 0.9)

23 ( 0.9) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.2) 8.9 13.9 3.4 ( 0.9)

24 ( 0.9) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.2) 8.2 12.1 5.0 ( 0.9)

25 ( 0.9) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.2) 8.7 10.1 3.9 ( 0.9)

26 ( 0.9) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.2) 9.0 7.7 2.6 ( 0.9)

27 ( 0.8) ( 0.5) ( 0.4) ( 0.3) ( 0.2) 0.2 ( 0.2) ( 0.2) 11.2 8.9 2.4 ( 0.9)

28 ( 0.8) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.2) 14.2 9.6 2.3 ( 0.9)

29 ( 0.8) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.2) ( 0.3) 22.0 9.2 2.4 ( 0.9)

30 ( 0.7) ( 0.5) ( 0.4) ( 0.3) ( 0.2) ( 0.2) ( 0.3) 22.8 8.1 2.1 ( 0.9)

31 ( 0.7) ( 0.4) ( 0.3) ( 0.2) ( 0.4) 8.6 2.1

Sum (35.6) (17.0) (12.6) (10.2) ( 8.4) ( 6.9) ( 4.6) ( 5.7) (252.1) 672.4 176.8 (33.3) 1,235.7

Sum of Measured Values 5.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 230.8 672.4 176.8 12.8 1098.4

Sum of Estimated Values (30.0) (17.0) (12.6) (10.2) ( 8.4) ( 6.9) ( 4.6) ( 5.7) ( 21.4) ( 0.0) ( 0.0) (20.4) (137.4)

% Measured 16% 0% 0% 0% 0% 0% 0% 0% 92% 100% 100% 39% 89%
14

1992 MASS BALANCE EVALUATION

Mass Balance Measurement Errors

Mass balance analysis seeks relatively small net changes in a system where

accumulation and ablation are large. Because of this, even small measurement errors can

significantly change the result, including the sign of the result. Furthermore, mass balance

measurement errors are difficult to treat analytically because of problems inherent in

sampling and extrapolation. Uncertainties in the mass balance determination at index

sites (the sampling points) arise from a combination of the uncertainties in determining

stake measurements, snow and firn densities, snow depths, and quantities of internal

accumulation. Indeed, many uncertainties must be estimated because there are an

insufficient number of independent samples to warrant error analysis; for example,

seldom are there more than two balance-motion stakes at an index site or more than one

snow-density pit. Uncertain at this time is the error introduced by extrapolating from a

few index-site values to glacier-wide and basin values. An independent assessment of

long-term glacier volume change by means of profile surveying and photogrammetric

mapping is under way to assess this error and, if necessary, revise the algorithm for

extrapolating glacier-wide balance from index-site values. Error estimates are included in

tabular data in this report.

Balance at Specific Sites

Measured winter snow balance, maximum winter snow balance, net mass balance,

and the annual mass balance are determined at each index site using largely traditional

methods (Østrem and Brugman, 1991 and Østrem and Stanley, 1969) and the stake, pit,

probing, coring, and meteorological data (tables 6, 7, and 8; fig. 3).

One departure from the traditional methods is our application of stake geometry

corrections that affect not only the stake position for motion (“Ice Motion Measurement

and Errors” section), but also the height on the stake of the glacier surface, b ́ (table 6).

After the position of the bottom of the stake is calculated using the stake’s geometry, the

height of the point on the glacier surface directly above the stake bottom is calculated and

used as a corrected b ́ as if the stake were vertical. The local glacier surface slope is

measured during every field visit for use in this calculation. These stake b ́ corrections

typically change our balance determinations by about 5 cm, but occasionally up to 0.5 m.

Also a departure from traditional methods is our procedure for making and using

multiple measurements of the height of a specific summer surface on a given stake to

both understand and to reduce the balance errors at a single site. For example, we

typically measure the snow depth and the stake height of the snow (glacier) surface in the

fall after the formation of the summer surface and again during the winter or spring,

giving us two measurements of the stake height of the same summer surface. If the

measurements were made in the accumulation zone, a third measurement of this stake

height of the summer surface can be made the following fall by subtracting the measured

snow depth and firn depth from the stake height of the glacier surface. Because of

measurement error, these successive measurements of the height of a specific summer
15

surface on a given stake are usually different, yet, barring stake slip, the height of the

summer surface on a given stake should not have changed. The interpretation that the

differing stake measurements are the result of measurement error is reinforced by the

observation that multiple measurements vary randomly, sometimes increasing and

sometimes decreasing. The multiple measurements are combined using a weighted

average. The weight for each measurement is proportional to the number of observations

that went into the measurement. For instance, a measurement that uses 20 snow-depth

probings is given twice the weight of a measurement with 10 snow-depth probings. The

weighted-average stake height of a specific summer surface is then used for all

calculations of balance relative to that summer surface.

The temporal extrapolations between measurements necessary to determine estimated

index-site balances, such as maximum winter balance and annual balance, are determined

using a simple linear model that relates the recorded air temperature and precipitationgage catch to glacier balance at each index site. The temperature is lapsed from the

recorder altitude to each of the index-site altitudes using the wet adiabatic lapse rate of

0.66°C per 100 m. Using the lapsed temperatures, the model estimates glacier ablation at

the rate of about 5 mm water equivalent per degree Celsius above 0°C per day. Glacier

accumulation is estimated by the model to be about 1.5 times the precipitation-gage catch

when the temperature is below +1.8°C. The melt (or ablation) rate and the precipitation

catch multipliers are not fixed, but are chosen to match measured balances on the glacier

at the index sites.

Area-Averaged Balances

The index-site balance values are combined using weighting factors to yield glacierwide index values that approximate the average balances for the glacier area:

b ̄ = 0.196 (bA) + 0.224 (bB) + 0.580 (bD)

where b ̄ is the glacier-averaged balance and bA, bB, and bD are measured index-site

balance values. The weighting factors, 0.196 for site A, 0.224 for site B, and 0.580 for

site D, are derived by splitting the glacier into three sub-areas (index regions) at altitudes

midway between the index sites (table 2). The percentage of total glacier area in each

index region is the weighting factor for the index site within that region. For this method

to be valid, the index-site balance value should equal the average balance in the index

region.

This weighted, index-site method was used to reassess the 1966 and 1967 measured

winter snow balance and annual firn-and-ice balance data published by Meier and others

(1971) and by Tangborn and others (1977) (table 9). The annual firn and ice balance was
depth, snow density, and snow temperature data for sites A, B, and D at Gulkana Glacier

t the year the stake was installed; letter (A, B, D) represents the site on the glacier; a number following the letter is used to differentiate multiple stakes installed at the

ate snow), snow on top of the current year’s summer surface, occurs only after the summer surface has formed. Observed b’, the average stake height of the glacier

 of the stake. b*, stake height of surveyed point on the stake near b’. b**, calculated height of the glacier surface directly above the stake bottom (i.e. as if the stake

be applied to correct b’ for stake lean, bend or bow. Total stake slip, cumulative distance the stake bottom has moved into the glacier since installed, it is generally

 fixed in the glacier. Best b’, observed b’ corrected for stake lean, bend, bow, and/or slippage. Stake d(s), snow depth as determined from the best b’ and previous or

 stake height of the summer surface. Pit d(s), snow depth measured in snow pit. McCall d(s), snow depth measured with a McCall snow sampler, a small-diameter

nowpack. Probe d(s), snow depth measured by probing to the summer surface with a metal rod. Mean d(s), average snow depth. s.e. d(s), standard error of snow depth.

s. Snow density, measured in snow pit, by McCall snow sampler, or estimated and mean density. Summer-surface temperature, observed with dial (±1.0°C) or digital

ed and the mean temperature. m, meter; kg/L, kilograms per liter]

Stake Readings & Data S n o w D e p t h S n o w D e n s i t y Summer Surf. Temp.

Obs. b’ Total Best 

ound No Lean Surveyed Diff. Stake Stake Stake Pit McCall Probe Mean s.e. Pit McCall Est. Mean Obs. Est.

Left Correct. b* b** b*-b** Slip b’ d(s)

d(s) n d(s) n d(s) n d(s)

d(s) n

(m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (kg/L) (kg/L) (kg/L) (kg/L) (degrees Celsius)

6/6 2.52 2.51 2.51 0.00 0.00 2.52 0.00

 0.30 0.30

9/9 2.80 0.00 2.80 0.44 26 0.44 0.02 26 0.30 0.306/6 4.05 0.00 4.05 1.69 1.69 0.30 0.30

6/3 3.95 3.93 3.95 0.02 0.00 3.97 1.63 2 1.63 0.00 2 0.32 0.32

0/12 10.78 10.77 10.80 0.03 0.00 10.81 1.63 2 1.63 0.00 2 0.32 0.32

7.24 8.18 8.15 0.03 0.00 7.21 0.00

9/10 6.59 8.18 8.15 0.03 0.00 6.56 0.17 2 0.27 20 0.26 0.03 22 0.30 0.30

 0.30 0.30

10/9 7.49 6.60 6.58 0.02 0.00 7.47 1.58 1 1.45 15 1.46 0.08 16 0.37 0.37 - 4.3

0/9 10.48 10.47 10.49 0.02 0.00 10.50 3.31 20 3.31 0.04 20 0.42 0.42

2/12 6.88 0.00 6.88 0.00

2/12 7.78 7.80 7.82 0.02 0.00 7.80 0.97 1 0.89 21 0.90 0.02 22 0.32 0.32

12/9 9.47 9.52 9.57 0.05 0.00 9.52 2.46 2 2.35 10 2.37 0.01 12 0.37 0.37

7.50 0.00 7.50 0.51 0.51 0.50 0.50

9/9 7.22 6.88 6.90 0.02 0.00 7.24 0.25 0.25 0 0.52 0.529/9) 7.11 7.11 7.13 0.02 0.00 7.13 0.66 1 0.68 17 0.68 0.02 18 0.27 0.27

1/11 8.64 8.63 8.67 0.04 0.00 8.68 2.31 1 2.40 3 2.29 20 2.30 0.03 24 0.37 0.37 0.37 - 3.2
depth, snow density, and snow temperature data for sites A, B, and D at Gulkana Glacier--Continued

Stake Readings & Data S n o w D e p t h S n o w D e n s i t y Summer Surf. Temp.

Obs. b’ Total Best 

ound No Lean Surveyed Diff. Stake Stake Stake Pit McCall Probe Mean s.e. Pit McCall Est. Mean Obs. Est.

Left Correct. b* b** b*-b** Slip b’ d(s)

d(s) n d(s) n d(s) n d(s)

d(s) n

(m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (kg/L) (kg/L) (kg/L) (kg/L) (degrees Celsius)

0/9 7.09 7.09 7.10 0.01 0.00 7.10 3.68 3.68 0.40 0.40 - 4.0

9/11 6.37 6.38 6.37 0.01 -0.18 6.18 1.18 1 1.18 1 0.32 0.32

1/11 8.50 8.48 8.53 0.05 -0.18 8.37 3.29 1 3.32 5 3.32 0.07 6 0.35 0.35 - 4.6

- 4.6

1/11 6.95 -0.50 6.45 1.36 1.36 0 0.50 0.50 0.0

1/11 7.30 7.31 7.33 0.02 -0.50 6.82 0.84 1 0.87 5 0.86 0.02 6 0.24 0.24 0.0

1/11 8.85 8.85 8.84 0.01 -0.50 8.34 2.36 1 2.53 8 2.51 0.06 9 0.36 0.36 - 4.8

change 7.34 7.35 7.38 0.03 -0.81 6.56 0.68 0.68 0.50 0.50 0.0

11/9 6.09 6.05 6.04 0.01 -0.85 5.23 0.00 0.0
 of stake data with firn depth, firn density, and ice data for sites A, B, and D at Gulkana Glacier

f the stake. Depths are measured from the glacier surface. Initial values are those at the beginning of the hydrologic year. Obs., observed values on a given date,

the best stake b’ and multiple snow or firn depth observations. b0’, initial average stake height of the glacier surface within a 50-meter radius of the stake, in meters. ss1,

n from the glacier surface (this is typically a bare ice surface in the ablation zone and a firn surface in the accumulation zone); ss2, second glacier summer surface down

ypically a firn surface; multiple summer surfaces only occur in the accumulation zone of the glacier. Mean heights average stake heights of a given stratigraphic surface

different dates. d(nf), new firn depth, in meters. Mean depths average all pit, McCall, and probing depths for a given date. s.e. is standard error. n, number of

e between the observed value on a given date and the mean value for that date, a good unbiased indication of the error in the stake height and snow and firn depth data

ters. m, meter; kg/L, kilograms per liter]

Height of Top of 1st Firn Depth to Bottom of 1st Firn Layer Firn Density Height of 1st Firn Bottom Height of Top of Ice

itial Obs. Mean Stake Pit McCall Probe Mean s.e. Pit Est. Mean Initial Obs. Mean diff. Initial Obs. Mean

0’ss1 b ’ss1 b ’ss1 ss1 Diff. d (nf) d (nf) n d (nf) n d (nf) n d (nf) d (nf) n b 0’ss2 b ’ss2 b ’ss2 ss2 Diff. b 0’ss1 b ’ss1 b ’ss1 ss1 Diff.

(meters) (m) (m) (m) (m) (m) (m) (kg/L) (kg/L) (kg/L) (meters) (meters)

 6.16 2.52 2.52 0.00 6.16 2.36 2.36 2.36 2.36 0.00 2.36 2.36 2.34 2.36 0.02 9.18 9.18 9.18 9.18 7.21 7.21 9.18 6.30 6.18 0.12 9.18 6.18 6.18 6.01 6.18 0.17 7.19 7.19 7.19 7.19 6.88 6.99 0.11 7.19 6.99 6.99 6.90 6.99 0.09 6.99 7.15 6.99 0.16 6.99 6.99 6.99 6.99 6.99 6.45 6.41 0.04 6.99 6.41 6.41 6.38 6.41 0.03

3.42 3.42 3.42 4.01 1 4.00 13 4.00 0.05 14 3.10 3.10 3.10 0.00

3.42 5.04 0.51 3.10 3.42

5.09 5.00 5.09 0.09 2.59 1 2.78 12 2.76 0.09 13 0.51 0.51 3.42 3.42 3.42 0.005.09 5.05 5.09 0.045.09 5.095.09 5.09

5.09 5.96 5.88 1.58 1 1.74 2 1.68 0.06 3 0.54 0.54 3.42 5.14 5.09 0.05

5.09 5.88 0.54 0.54 3.42 5.09

5.88 5.83 5.88 5.095.88 5.88 5.88 0.61 0.61 5.09

5.88 5.23 5.23 0.61 0.61 5.09
 of stake data with mass-balance calculations for sites A, B, and D at Gulkana Glacier

 initial ice balance; b(s), snow balance; b1(i), late ice balance; b1(ls), late snow balance; b(f), firn balance; b(k), internal accumulation; b(i), ice balance; bn, net balance;

water equivalent (See Mayo and others (1972) for detailed explanation of this terminology)]

 W a t e r E q u i v a l e n t B a l a n c e s

Init. Init. Late Late Int.

Snow Ice Snow Ice Snow Firn Acc. Ice Net Annual

b o(s) b o(i) b (s) b 1 (i) b 1 (ls) b (f) b (k) b (i) b n b a

(m w e ) (m w e ) (m w e ) (m w e ) (m w e ) (m w e ) (m w e ) (m w e ) (m w e ) (m w e ) Special Notes

0.00 0.00 0.00 0.00 0.00 0.00 - 3.28 -3.28 Stake in edge of moraine, but not at high point; ablation 

does not appear to be significantly different right at stake.

0.00 0.04 0.00 0.04 0.00 0.00 - 3.42 0.04 Est. annual balance

0.04 0.00 0.13 0.00 0.00 0.00 0.00 0.00 0.13 0.090.04 0.00 0.51 0.00 0.00 0.00 0.00 - 2.12 -1.61 -1.650.04 0.00 0.52 0.00 0.00 0.00 0.00 0.00 0.52 0.480.04 0.00 0.52 0.00 0.00 0.00 0.00 0.00 0.52 0.480.04 0.00 0.58 0.00 0.00 0.00 0.00 0.00 0.58 0.54 Est. maximum winter snow balance

0.04 0.00 0.00 0.00 0.00 0.00 0.00 - 1.77 -1.77 -1.81

0.04 0.00 0.08 0.00 0.08 0.00 0.00 - 2.70 0.08 -2.660.04 0.00 0.08 0.00 0.08 0.00 0.00 - 2.70 0.08 -2.66 Est. annual balance

0.08 0.00 0.54 0.00 0.00 0.00 0.00 0.00 0.54 0.46

0.00 1.39 0.00 0.00 0.00 0.00 0.00 1.39

0.00 0.00 0.00 0.00 0.00 0.00 - 0.18 -0.18

0.00 0.00 0.00 0.22 0.00 0.00 - 0.18 0.00 Est. annual balance

0.22 0.00 0.29 0.00 0.00 0.00 0.00 0.00 0.29 0.07

0.22 0.00 0.88 0.00 0.00 0.00 0.00 0.00 0.88 0.66

0.22 0.00 0.96 0.00 0.00 0.00 0.00 0.00 0.96 0.74 Est. maximum winter snow balance

0.22 0.00 0.26 0.00 0.00 0.00 0.00 0.00 0.26 0.04

0.22 0.00 0.13 0.00 0.00 0.00 0.00 0.00 0.13 -0.090.22 0.00 0.19 0.00 0.19 0.00 0.00 - 0.52 0.19 -0.550.22 0.00 0.19 0.00 0.19 0.00 0.00 - 0.52 0.19 -0.55 Est. annual balance

0.19 0.00 0.85 0.00 0.00 0.00 0.00 0.00 0.85 0.66

0.00 1.47 0.00 0.00 0.00 0.00 0.00 1.47

0.00 0.00 0.30 0.83 0.16 0.00 0.99 Est. annual balance

0.30 0.00 0.35 0.00 0.00 0.00 0.00 0.00 0.35 0.05

0.30 0.00 1.15 0.00 0.00 0.00 0.00 0.00 1.15 0.850.30 0.00 1.25 0.00 0.00 0.00 0.00 0.00 1.25 0.95 Est. maximum winter snow balance

0.30 0.00 0.68 0.00 0.00 0.00 0.18 0.00 0.86 0.56

0.30 0.00 0.22 0.00 0.22 0.43 0.18 0.00 0.83 0.530.30 0.00 0.22 0.00 0.22 0.43 0.18 0.00 0.83 0.53 Est. annual balance

0.22 0.00 0.89 0.00 0.00 0.00 0.00 0.00 0.89 0.67

0.22 0.00 0.34 0.00 0.00 0.00 0.19 0.00 0.53 0.310.22 0.00 0.00 0.00 0.00 0.00 0.19 - 0.40 -0.21 -0.43 91 & ’92 sum m er surface sawdust patches exposed
20

Table 9. Mapped and weighted index-site balances for 1966 and 1967

[Mapped values for 1966 from Meier and others (1971) and for 1967 from Tangborn and others (1977)]

1966 1967

balance balance

Glacier averaged balance quantity & method (meters) (meters)

b m(s), Measured winter snow balance

Mapped value 1.00 ± 0.15 1.05 ± 0.12

Weighted index-site value 1.13 ± 0.33 1.08 ± 0.33

b a(fi), Annual firn & ice balance

Mapped value -0.21 ± 0.10 -0.28 ± 0.14

Weighted index-site value -0.01 ± 0.46 -0.29 ± 0.46

used for the comparison because it is similar to the net balance, whereas insufficient netbalance data were published for 1966 and 1967 to allow a direct net-balance comparison.

The errors associated with the weighted index-site values are large because the current

index-site locations were not measured in 1966 or 1967. Hence, the index-site values

were picked by interpolating from 1966 and 1967 balance contour maps. The errors are

larger for the annual firn-and-ice balance because the contour interval on those maps is

greater. The results of the comparison show that the weighted index-site values are

consistently high, but within the estimated errors. Figures 8 and 9 show a detailed

comparison for 1966 and 1967 of the estimated index-site balances, the mapped balances

with altitude, and the average balances for the regions associated with each index site.

Only index site B seems to consistently bias the data by overestimating the balance for its

region. Given the variability of balance gradients we have observed, it is not justified to

adjust the weighting factors on the basis of only 2 years of detailed data. The weighted,

index-site method should be verified and (or) adjusted from an independent assessment of

glacier mass balance for many years or from a long-term photogrammetric or surveyed

volume change of the entire glacier. Until this has been done, it is not possible to

determine the error in glacier-averaged balances, as determined by the weighted, indexsite method. From the 1966 and 1967 data, we estimate that glacier-averaged balance

values have an error of ±0.2 m.
21

-4

-3

-2

-1

0

1

2

1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500

ALTITUDE, IN METERS

BALANCE, IN METERS

Mapped ba (fi)

Index Site b a (fi)

Averaged b a (fi) for Index Region

Annual Firn & Ice Balance

_

_

0

1

2

3

1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500

ALTITUDE, IN METERS

GLACIER AREA, IN 

SQUARE KILOMETERS

Area/Altitude Distribution

Region A Region B Region D

-1

0

1

2

1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500

ALTITUDE, IN METERS

BALANCE, IN METERS

Measured Winter Snow Balance

Mapped b m (s)

Averaged b m (s) for Index Region

Index Site b m (s)

_

_

Figure 8. Altitude distribution of measured winter snow balance, bm(s), annual firn and

ice balance, ba(fi), and glacier area of Gulkana Glacier for 1966 (data from

Meier and others, 1971). (Index-site values and error bars are estimated from

balance contour maps by Meier and others (1971). Average balance values for

index regions are calculated by integrating the balance curve with the

area/altitude curve for the region of each index site.)
22

-1

0

1

2

1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500

ALTITUDE, IN METERS

BALANCE, IN METERS

Measured Winter Snow Balance

Mapped b m (s)

Average b m (s) for Index Region

Index Site b m (s)

_

_

-4

-3

-2

-1

0

1

2

1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500

ALTITUDE, IN METERS

BALANCE, IN METERS

Mapped b a (fi)

Index Site b a (fi)

Average ba (fi) for Index Region

Annual Firn & Ice Balance

_

_

0

1

2

3

1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500

ALTITUDE, IN METERS

GLACIER AREA, IN 

SQUARE KILOMETERS

Area/Altitude Distribution

Region A Region B Region D

Figure 9. Altitude distribution of measured winter snow balance, bm(s), annual firn and

ice balance, ba(fi), and glacier area of Gulkana Glacier for 1967 (data from

Tangborn and others, 1977). (Index-site values and error bars are estimated

from balance contour maps by Tangborn and others (1977). Average balance

values for index regions are calculated by integrating the balance curve with the

area/altitude curve for the region of each index site.)
23

Weather in 1991-1992

The 1992 net balance year began on September 6, 1991, when below-freezing

temperatures and snow accumulation started on the upper part of the glacier. The seasonal

stream runoff recession began during late September 1991. The last day of open-water

stage at the stream-gaging station at 1,125 m altitude was recorded on October 3, 1991.

The lowest daily-mean winter air temperature was -27°C on February 27, 1992. Winter

(October 1 to April 30) precipitation-gage catch totaled 308 mm. As is typical, no surface

melt occurred on the glacier from about October 1 to mid-April. The 1992 mass balance

maximum occurred about May 19 after surface melting on the lower part of the glacier

and the seasonal rise in runoff had presumably begun. The final mass balance minimum

occurred about August 17, 1992, when the entire glacier was observed covered by fresh

snow that did not melt; the seasonal runoff recession began after August 25, 1992, when

the season's last precipitation-caused runoff peak ended. The last day of open-water stage

was recorded on September 9, 1992. The total runoff for the 1992 water year was 65

percent of the mean for the period of record (1966-78 and 1989-current).

Measured and Maximum Winter Snow Balances1

The glacier-average measured winter snow balance, b ̄ m(s), is the balance measured to

the summer surface in late winter or spring (Mayo and others, 1972). It was 0.97 m on

March 26, 1992 (table 10). This value was derived by using the weighted index-site

method and the March field visit data (tables 6, 7, and 8). The maximum winter snow

balance, b ̄ w(s), is the maximum snow mass during the balance year and may occur either

before or after the measured winter snow balance (Mayo and others, 1972). It generally

occurs after the time of the measured winter snow balance at Gulkana Glacier and is

determined by estimating the balance increment at each index site between the time of the

measured winter snow balance and the time of the maximum winter snow balance. The

1992 glacier-average maximum winter snow balance of 1.05 m occurred about May 19,

1992 (table 10).

Net Balance

Net balance is the change in snow, firn, and ice storage between times of minimum

glacier mass (Mayo and others, 1972). The net balance, bn, at each index site is calculated

directly from balance-motion stake, pit, and probing data. Field measurements made near

the end of the balance year are confirmed with measurements during the next balance year

before final values are assigned (tables 6, 7, and 8). The 1992 net balance year began on

about September 8, 1991, and ended on about August 17, 1992; the glacier-average net

balance was -0.29 m (table 10).

 1

 Mayo and others (1972) define three “winter” balance values in the stratigraphic system: the

measured winter snow balance, b ̄ m(s); the maximum winter snow balance, b ̄ w(s); and the winter balance, b ̄ w.

The World Glacier Monitoring Service (WGMS) publishes a winter balance that is not rigorously any of

these, but is most closely related to the measured winter snow balance, b ̄ m(s).
24

Table 10. Area-integrated measured winter snow, maximum winter snow, annual, and net

balance quantities for Gulkana Glacier and Gulkana Glacier basin

Balance

Balance quantity and site or area (meters)

b m(s), Measured winter snow balance on March 26, 1992

Site A, 1373 m. 0.52

Site B, 1685 m. 0.88

Site D, 1837 m. 1.15

Glacier Average 0.97

b w(s), Maximum winter snow balance on May 19, 1992

Site A, 1373 m. 0.58

Site B, 1685 m. 0.96

Site D, 1837 m. 1.25

Glacier Average 1.05

b a, Annual balance, October 1, 1991 - September 30, 1992

Site A, 1373 m. -2.65

Site B, 1685 m. -0.74

Site D, 1837 m. 0.53

Glacier Average -0.38

b n, Net balance, September 8, 1991 - August 17, 1992

Site A, 1373 m. -2.70

Site B, 1685 m. -0.52

Site D, 1837 m. 0.61

Glacier Average -0.29

Summer Balance

The summer balance, b ̄ s, was not defined by Mayo and others (1972); we follow the

definition by United Nations Educational, Scientific, and Cultural Organization/

International Association of Scientific Hydrology (1970) which says it is the algebraic

difference between the winter balance and the net balance, b ̄ n. Following their definition

of winter balance, we use the corresponding term from Mayo and others (1972), b ̄ w(s), so

that:

b ̄ s = b ̄ n - b ̄ w(s) = -1.34 m

Annual Mass Balance

Annual mass balance is the change in snow, firn, and ice storage between the

beginning (October 1, 1991) and end (September 30, 1992) of the hydrologic year.

Evaluation of the 1992 annual balance required estimating two adjustment quantities. At

the beginning of the hydrologic year, the initial snow balance at each index site, b0(s),

was estimated using field data from the balance-motion stakes and air temperature and

precipitation data. At the end of the hydrologic year, the final late snow balance at each

index site, b1(ls), was estimated using field data from the balance-motion stakes and air

temperature and precipitation data. The 1992 annual balance at each index site, ba, is
25

derived from the net balance and adjustment quantities: ba = bn - b0(s) + b1(ls) (table 8).

The index-site annual balances are combined using the weighted index-site method to

yield the 1992 annual balance of -0.38 m (table 10).

Accumulation Area Ratio and Equilibrium Line Altitude

The accumulation area ratio (AAR) is the area of new firn, superimposed ice, and any

area where internal accumulation exceeds old firn loss, i.e. the accumulation area, divided

by the total glacier area. The 1992 AAR was 0.59, based on a glacier surface area of

19.3 km2, which was reported for 1967 by Tangborn and others (1977).

The equilibrium line altitude (ELA), the average altitude where snow ablation equals

snow accumulation, seldom crosses a glacier at a single altitude. The Gulkana Glacier

ELA can be extremely complicated and would require well-timed vertical or high-angle

oblique aerial photography to define accurately. Obtaining this kind of photography near

the time of formation of the ELA on a consistent basis year after year was judged

impractical. Therefore, it was decided that calculating the ELA by linear interpolation

from the balance-altitude curve for the three index sites would be a more consistent and

meaningful method in the long term. The 1992 ELA for Gulkana Glacier was 1,755 m.

The Gulkana Glacier terminus position was not measured during 1992.

The surface area of Gulkana Glacier and other small glaciers in the Gulkana Glacier

basin has not been determined since 1967. Therefore, the reported areas and area ratios

will change when a reassessment is made because obvious retreat of the terminus and

thinning have occurred since 1967.

ICE MOTION MEASUREMENT AND ERRORS

Surface ice displacements near the fixed index sites are measured during each field

visit by optical surveying. Balance-motion stakes are installed at a location equivalent to

about one year’s flow displacement upstream from each index site. Replacement stakes

are installed every year or two. Thus, the stakes are kept within one year’s displacement

of the index site (typically less than 80 m) to maximize the year-to-year comparability of

the motion data. The optical surveying techniques have been described by Mayo and

others (1979) and Mayo and Trabant (1982). Reported velocities (table 11) are the

average velocities derived from the linear displacement of the bottom of the stake divided

by the measurement period. The bottom of the stake is used for the velocity determination

because stakes installed vertically are usually found later to be leaning and on rare

occasions bent or bowed. Movement of the bottom of the stake is believed to be the most

representative of the motion of the glacier surface. Hence, reported stake motion data

have been corrected for changes in stake geometry.

The position of the bottom of the stake is determined by surveying two points on each

stake (one at the glacier surface and the other at 1 or 2 m higher on the stake) and then

calculating the location of the stake bottom using a linear (lean), bent, or bowed stake

geometry. In the long history of field observations at Gulkana Glacier, it has been rare to
ons, stake lean corrections, and ice motion determined from optical surveys

t the year the stake was installed; letter (A, B, D) represents the site on the glacier; a number following the letter is used to differentiate multiple stakes installed at the

 stake lower target is where the stake intersects the glacier surface. 

Xt, Yt, Zt, stake upper target is a point on the stake 1.5-2.0 m above the glacier surface. 

Ht is the

bove the stake bottom as measured along the stake. θ is the down-dip direction with zero east and positive counterclockwise. φ is the dip angle with zero horizontal and

: lean, treats the stake as a linear segment; bend, treats the stake as multiple linear segments; bow, treats the stake as a combination of linear and arc segments. b* is the

er target above the stake bottom as measured along the stake. b** is the calculated height of the glacier surface directly above the stake bottom (i.e. as if the stake were

he stake bottom has moved into the glacier; it is generally assumed that the stake bottom is fixed in the glacier. dXYZ is the total three-dimensional displacement of the

ents. Annual velocity is the stake displacement divided by the period between measurements. Horizontal displacement angle is measured positive counter-clockwise,

nt angle is measured positive up from horizontal. m, meters; m/yr, meters per year]

ower Target Stake, Upper Target Glacier Surface Solution Stake Angles Stake Bottom Stake Annual Displ. Angles

Yg Zg Xt Yt Zt Ht θ φ Type θ φ Xs Ys Zs b* b** Slip dXYZ Velocity Horiz. Vert.

eters) (meters) (grad) (grad) (meters) (meters) (m) (m/yr) (grad)

463.64 1,376.79 3,821.46 4,463.67 1,378.89 10.00 -159.76 -7.46 lean - 15.60 -96.25 3,822.03 4,463.53 1,368.90 7.90 7.92455.62 1,371.39 3,814.78 4,455.60 1,373.38 4.50 -166.31 -6.81 lean 37.43 -98.85 3,814.85 4,455.65 1,368.88 2.51 2.51 10.66 27.60 -147.05 - 0.14448.29 1,373.13 3,807.87 4,448.28 1,375.19 6.00 -151.11 -7.55 lean 4.24 -95.36 3,808.31 4,448.31 1,369.21 3.93 3.95 9.84 17.78 -146.36 2.14460.43 1,375.05 3,818.62 4,460.44 1,376.28 12.00 -151.11 -7.55 lean - 9.03 -96.34 3,819.30 4,460.34 1,364.30 10.77 10.80453.81 1,373.10 3,813.19 4,453.86 1,373.92 9.00 -151.45 -6.86 lean - 39.49 -93.35 3,813.95 4,453.31 1,364.96 8.18 8.15 8.86 27.41 -141.40 4.80451.40 1,371.18 3,810.78 4,451.51 1,373.57 9.00 -136.16 -9.97 lean - 29.52 -93.47 3,811.60 4,451.10 1,364.61 6.60 6.58 3.25 19.13 -151.87 - 6.87

4,764.86 7,439.53 1,692.44 9.00 lean 4,764.86 7,439.53 1,683.44 22.36 57.47 -131.56 - 6.03

435.54 1,690.81 4,762.54 7,435.45 1,693.01 10.00 -127.83 -6.31 lean 86.08 -97.33 4,762.63 7,435.86 1,683.02 7.80 7.82 4.32 50.86 -134.74 - 6.25416.45 1,690.81 4,752.53 7,416.33 1,692.28 11.00 -130.41 -6.22 lean 70.48 -94.21 4,752.98 7,417.22 1,681.33 9.52 9.57 21.05 44.93 -130.43 - 5.11399.58 1,686.44 4,744.42 7,399.46 1,688.56 9.00 -129.84 -6.35 lean 120.48 -96.21 4,744.25 7,399.97 1,679.57 6.88 6.90 19.42 60.07 -129.81 - 5.77391.58 1,685.49 4,740.72 7,391.52 1,687.38 9.00 -131.05 -6.27 lean 79.52 -97.87 4,740.82 7,391.81 1,678.38 7.11 7.13 8.94 52.63 -125.36 - 8.49371.53 1,685.15 4,731.15 7,371.40 1,687.01 10.50 -122.31 -5.99 lean 68.55 -94.96 4,731.54 7,372.13 1,676.55 8.63 8.67 21.83 42.16 -128.04 - 5.36

354.21 1,840.47 6,011.76 7,354.71 1,841.94 7.00 174.07 -7.06 lean - 69.47 -76.69 6,012.92 7,352.49 1,835.40 5.43 5.24 - 0.41 10.13 49.30 168.11 - 6.39368.24 1,836.11 5,987.07 7,368.40 1,837.79 6.00 173.60 -6.75 lean - 70.48 -93.25 5,987.35 7,367.83 1,831.82 4.31 4.32 - 0.41 30.03 63.36 165.58 - 7.60

324.84 1,846.66 6,059.87 7,324.84 1,848.57 9.00 174.07 -7.06 lean -98.67 6,060.06 7,324.84 1,839.57 7.09 7.10339.70 1,841.95 6,034.52 7,339.66 1,844.07 8.50 173.60 -6.75 lean 129.52 -98.66 6,034.44 7,339.82 1,835.57 6.38 6.37 29.95 63.19 166.31 - 8.53353.14 1,841.02 6,011.07 7,353.33 1,843.02 10.50 140.53 -7.90 lean - 41.37 -90.09 6,012.37 7,352.34 1,832.64 8.48 8.53 25.55 54.54 167.14 - 7.31368.66 1,835.61 5,984.37 7,368.67 1,837.30 9.00 159.02 -6.12 lean - 5.77 -95.85 5,984.95 7,368.62 1,828.32 7.31 7.33 32.17 65.23 165.90 - 8.59382.52 1,834.33 5,959.44 7,382.65 1,836.45 11.00 147.92 -6.01 lean - 22.06 -88.63 5,961.28 7,381.99 1,825.62 8.85 8.84 27.32 52.48 167.28 - 6.29
27

find melted-out stakes bent or bowed, so a “lean” geometry is generally assumed unless

the stake is severely tilted. Occasionally, when a stake is severely tilted, it is partly

excavated to determine if it is bent or bowed, and where. Bent or bowed geometries,

when they do occur, generally occur at or above the most recent summer surface.

Determining and measuring the stake geometry is an imprecise process. Stake

connectors, which join multiple 3-m stakes to make taller stakes, allow stake tilt of about

±1.5 grad at connectors. This translates into horizontal errors of ±0.15 m at the bottom of

the typical stake that extends about 6 m into the glacier. The uncertainty in determining

the stake’s geometry (lean, bend, or bow) is estimated to double this error, resulting in a

total error in the horizontal of ±0.3 m from geometric corrections. The bottom of the

stake (XsYs in table 11) is typically offset horizontally 0.3-1.5 m from the surveyed target

on the stake at the glacier surface (XgYg in table 11). Therefore, the geometric corrections

are significant and would typically lead to motion errors of 5-20 percent in the Gulkana

data if not corrected.

Location uncertainty is largely a result of the survey control net errors (GPS for

horizontal and optical surveying for vertical) and resection2

 survey errors. Combined,

these yield position errors of about ±0.15 m in the horizontal and ±0.05 m in the vertical.

Additionally, ice motion errors include the error in assuming a stake geometry and

extrapolating from surveyed points on the stake to the bottom of the stake. Measuring this

error would require digging up a statistically significant number of stakes, an

unreasonable task. We estimate the error of extrapolating to the bottom of the stake to be

±0.15 m, giving a total horizontal error for stake bottom positions of ±0.2 m. Vertical

errors are significantly less, about ±0.05 m. Hence, reported displacements have errors of

about ±0.3 m.

GLACIER SURFACE ALTITUDE MEASUREMENT AND ERRORS

Seasonal changes of the glacier surface altitude at each index site are measured during

each field visit (tables 12-13). At least three points on the glacier surface in the vicinity of

the index site are optically surveyed. One of the points is placed as closely as possible to

the index site. The mathematical plane defined by the three surveyed points is calculated

as an approximation to the local glacier surface. The altitude of this plane at the fixed

horizontal position of the index site is calculated to determine the index site altitude

(Mayo and Trabant, 1982).

Surveyed glacier-surface points typically have an altitude uncertainty of about

±0.05 m; this uncertainty is a combination of survey net errors and resection errors.

Additionally there is the possibility that the locations used to define the plane of the

glacier surface are not representative of the average glacier surface and hence

extrapolating along this plane to the index site introduces further error. The glacier

surface orientation and slope determinations have a small random variability that is used

to assess the magnitude of this error. While this error is site-specific depending largely on

 2

 Resection surveys are conducted with redundancy to allow estimation of their error. Typically, four or

five backsight targets are surveyed for each resection.
28

the local surface roughness of the glacier, an average glacier-surface-slope error of

0.5 grad was applied to the distance between the closest surveyed point and the index site.

This error combined with the surveying error yields an average error of ±0.15 m for the

index-site altitudes. Index-site errors are calculated separately for each measurement and

are included in tables 12-13.
face and summer-surface altitude measurements and analysis at index sites

on the glacier surface near the index site determined by optical surveying. 

Xi, Yi are the horizontal locations of the fixed index site; 

Zi is the calculated altitude of the

θ is the down-dip direction of the glacier surface, with zero east and positive counterclockwise; φ is the dip angle of the glacier surface with positive angles up from

oint” is the horizontal distance from the index site to the closest of points P, Q, or R. 

Zi error is the altitude error in 

Zi from combining the resection errors with the error

e altitude from the closest point to the index site assuming the glacier surface slope to be linear]

P Q R Index Site Glacier Surface Dist. to

Slope Closest Zi

Y Z X Y Z X Y Z Xi Yi Zi θ φ Point Error

meters) (meters) (meters) (meters) (grad) (meters)

455.62 1,371.39 3,804.40 4,463.27 1,370.84 3,787.83 4,442.69 1,368.19 3,825.10 4,447.27 1,371.89 -166.31 -6.81 13.25 0.11445.63 1,374.33 3,808.02 4,448.29 1,373.13 3,818.69 4,460.43 1,375.05 3,825.10 4,447.27 1,374.51 -151.11 -7.55 1.73 0.19464.55 1,375.04 3,816.52 4,411.83 1,369.26 3,813.26 4,453.81 1,372.14 3,825.10 4,447.27 1,372.58 -151.45 -6.86 13.53 0.22443.92 1,369.07 3,811.00 4,451.40 1,371.18 3,821.16 4,447.77 1,371.56 3,825.10 4,447.27 1,371.83 -136.16 -9.97 3.97 0.03441.34 1,373.96 3,804.50 4,444.38 1,372.22 3,820.25 4,449.24 1,373.78 3,825.10 4,447.27 1,374.01 -150.57 -6.77 5.24 0.05437.99 1,690.37 4,764.86 7,439.53 1,690.32 4,740.45 7,386.37 1,685.45 4,728.61 7,391.17 1,685.03 -148.68 -5.60 12.78 0.14428.94 1,689.75 4,762.56 7,435.54 1,690.81 4,740.45 7,386.37 1,685.45 4,728.61 7,391.17 1,685.38 -127.83 -6.31 12.78 0.10422.97 1,690.52 4,765.85 7,412.04 1,690.93 4,742.18 7,388.45 1,687.81 4,728.61 7,391.17 1,687.44 -130.41 -6.22 13.84 0.11361.52 1,679.62 4,774.92 7,370.67 1,685.39 4,727.68 7,417.12 1,687.40 4,728.61 7,391.17 1,685.13 -129.84 -6.35 25.97 0.20376.12 1,684.19 4,740.74 7,391.58 1,685.49 4,725.60 7,377.14 1,683.53 4,728.61 7,391.17 1,684.89 -131.05 -6.27 12.14 0.10391.00 1,686.90 4,731.22 7,371.53 1,685.15 4,738.00 7,382.62 1,686.35 4,728.61 7,391.17 1,686.81 -122.31 -5.99 3.37 0.03323.74 1,846.87 6,059.91 7,324.84 1,846.66 6,012.02 7,354.21 1,840.47 5,999.01 7,353.57 1,839.17 174.07 -7.06 13.03 0.11349.40 1,837.85 5,987.15 7,368.24 1,836.11 6,034.50 7,339.70 1,841.95 5,999.01 7,353.57 1,837.90 173.60 -6.75 4.74 0.05364.10 1,836.90 6,011.32 7,353.14 1,841.02 6,011.82 7,363.68 1,840.00 5,999.01 7,353.57 1,840.06 140.53 -7.90 12.32 0.11

1,837.49

355.91 1,836.97 5,984.48 7,368.66 1,835.61 6,008.16 7,360.11 1,837.93 5,999.01 7,353.57 1,837.60 159.02 -6.12 6.90 0.06362.13 1,839.44 6,007.48 7,349.97 1,839.66 5,959.80 7,382.52 1,834.33 5,999.01 7,353.57 1,838.87 147.92 -6.01 9.20 0.07

9.69 0.10
n of glacier surface and summer-surface altitude measurements and analysis at index sites

cribed in headnote for table 11. Best b’ is the height of the glacier surface directly above the stake bottom. Change in b’ is the change from the previous measurement to

gence is the change in 

Zi minus the change in b’ divided by the time in years. Snow depth is the depth from the glacier surface to the summer surface (see table 6). 

Z

h. m/yr, meters per year]

Stake 1 Stake 2 Stake 3

Z

Change Change Change Snow Summer

Date Name Best b’ b’ Name Best b’ b’ Name Best b’ b’ Emerg. Depth Surface

yy/mm/dd (meters) (meters) (meters) (m/yr) (meters)

91/09/06 90-A2 - 0.36 -5.25 91-A 2.52 -5.40 2.39 1,371.8992/03/26 91-A 3.97 1.45 92-A 10.81 2.11 1.63 1,372.8892/07/22 92-A 7.21 -3.60 5.17 1,372.5892/09/22 92-A 6.56 -0.65 -0.59 0.26 1,371.57

93/03/31 93-A 10.49 93-A2 10.43 92-A 7.47 0.91 2.44 1.46 1,372.5591/09/06 91-B2 6.88 - 3.62 1.41 1,685.0391/10/07 91-B2 7.80 0.92 -6.71 0.90 1,684.4892/03/26 91-B2 9.52 1.72 0.73 2.37 1,685.0792/07/18 91-B2 7.24 - 2.28 -0.10 0.25 1,684.8892/09/22 91-B2 7.13 - 0.11 -0.72 0.68 1,684.2193/03/30 91-B2 8.68 1.55 0.71 2.30 1,684.5191/04/17 90-D2 4.86 0.71 91-D 7.10 1.07 1,839.1791/10/07 90-D2 3.94 - 0.92 91-D 6.18 - 0.92 -0.74 1.18 1,836.7292/03/26 91-D 8.37 2.19 -0.06 3.32 1,836.7492/07/18 91-D 6.45 - 1.92 -2.08 1.36 1,836.1392/09/22 90-D2 4.58 91-D 6.82 - 1.55 -1.85 0.86 1,836.7493/03/31 93-D 8.84 91-D 8.34 1.52 -0.48 2.51 1,836.36

Site A Site B Site D
31

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