COMPILATION AND ANALYSIS OF SNOWPACK DATA FOR THE LAKE
SUPERIOR BASIN
By
Paul C. Crocker
A REPORT
Submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE OF FORESTRY
MICHIGAN TECHNOLOGICAL UNIVERSITY
1999
ABSTRACT
The outflow from Lake Superior has been influenced by humans for over two
hundred years, and the U.S. Army Corps of Engineers (USACE) has regulated the level
of the Great Lakes for decades. Management plans require long-range forecasts of
precipitation, snow pack, and evaporation from the lake. Snow pack has an especially
large impact on lake levels, and therefore the mean snow water equivalent (SWE) of the
snow pack in the basin is of great interest to the USACE. The objective of this study was
to use a Geographic Information System (GIS) to estimate the mean or normal SWE for
sub-basins in the Lake Superior watershed. We investigated the availability, extent, and
quality of potential sources of snow pack data, and focused on those sources that
provided the most accurate snow depth and SWE data with the longest period of record.
The spatial and temporal extent of the data were determined, and methods were derived
to estimate mean SWE based upon relationships between snow depth and SWE. The
snow depth measurements recorded by the cooperative station network were converted to
SWE using the ratios of depth to SWE calculated from Canadian snow course and U.S.
first-order weather station archives. Mean SWE values were then estimated at bi-weekly
intervals for the entire basin by interpolating from the converted-SWE value point
coverages. The kriging algorithm was used for the interpolation. These methods take
advantage of the accuracy of direct SWE measurements and the dense distribution of
cooperative observer stations in the basin.
ii
TABLE OF CONTENTS
Abstract ............................................................................................................................... ii
Table of Contents ............................................................................................................... iii
Acknowledgments.............................................................................................................. iv
List of Tables ...................................................................................................................... v
List of Figures .................................................................................................................... vi
List of Appendices ........................................................................................................... viii
Introduction ......................................................................................................................... 1
Goals of this Study.......................................................................................................... 3
Data and Study Area ........................................................................................................... 4
Study Area ...................................................................................................................... 4
Gamma Survey Flight Data - SWE................................................................................. 7
NWS Cooperative Data - Snow Depth and SWE ......................................................... 10
Canadian Snow Courses and Cooperative Stations ...................................................... 13
Overview of Methodology ............................................................................................ 16
Calculation of Mean SWE Values ................................................................................ 17
Calculation of Confidence Intervals ............................................................................. 20
Comparison to Gamma Flight Data .............................................................................. 29
GIS & Applications ...................................................................................................... 30
Data Products ................................................................................................................ 33
Base Coverages ......................................................................................................... 33
Bi-weekly SWE Estimates ........................................................................................ 33
Gamma Survey Flights ............................................................................................. 34
Departures from Normal ........................................................................................... 34
Conclusions and Recommendations ................................................................................. 41
References ......................................................................................................................... 42
iii
ACKNOWLEDGMENTS
I would like to thank all of my family, friends, colleagues, and professors that
have made this project possible. My parents, Patricia M. Israel and Mark S. Crocker,
were pivotal in supporting my decision to further my education. Chris and Marge Donley
were equally supportive of me in this endeavor.
I cannot forget my many friends for their support, and for reminding me to take
those essential breaks from the lab. In particular, I’d like to thank Kristie Potter for the
many hours that she devoted to the project by helping me with the climate archives and
for her constant encouragement. Radley Watkins, Karen Owens, Robb and Becky
Cookman, Lyndon and D. Lawson Gerdes, Barbara Fillmore, Mary Jenkins, Aimee
Stephens, Phil Szorny, Colleen Riley, Leslie Jagger, David VanderMeulen, Carrie
Schaefer, Jennifer Fox, and many others deserve my thanks as well.
Mike Hyslop was invaluable by devoting his time, patience and skills to the
project and his guidance in my development as an analyst. My co-advisors, Dr. Dennis
L. Johnson and Dr. Ann L. Maclean, provided guidance and inspiration prior to and
during this project. My other committee members, Dr. David D. Reed and Dr. Henry
Santeford, were equally helpful throughout this process.
Doug Lawler at Ontario Hydro and Maurizzio Evangelista at Ontario Ministry of
Natural Resources were exceptionally helpful in supplying me with data for the Canadian
portion of the project. Finally, this project would not have been possible if not for the
support of the U.S. Army Corps of Engineers (Detroit District). Mr. Adam Fox and Mr.
Mathew McPherson were invaluable by providing feedback and suggestions throughout
the project. Their contributions are gratefully appreciated.
iv
LIST OF TABLES
1. Description of base coverages and their sources……………………………………….6
2. Bi-weekly mean SWE ratios (SD/SWE) for the Canadian snow courses. Values in
bold were estimated using linear regression……………………………………………..28
3. Comparison of coop stations with gamma surveys……………………………………30
4. Description of the advantages and limitations of each data source in estimating mean
Snow Water Equivalent (SWE) for bi-weekly time intervals……………………………38
v
LIST OF FIGURES
1. Compensating Works at Sault Ste. Marie…………………………………………….2
2. Study area and base coverages………………………………………………………..5
3. Gamma survey flight line locations in the Lake Superior region. ……….…….……..8
4. NWS First-order and cooperative stations in the Lake Superior region. ……………11
5. Canadian snow courses in the Lake Superior region. ……………………………….14
6. Canadian cooperative stations in the Lake Superior region. ………………………...15
7. Semivariogram created in Arc/Info used to determine
the area of influence of each first-order station. Range a illustrates the maximum
distance of influence was 165,000 meters……………………………………………….19
8. All SWE ratios on record for the first-order station in Sault Ste. Marie, MI….……...21
9. All SWE ratios on record for the snow course at Hawk Junction, ON. Note that
snow course measurements were only made at bi-weekly intervals……………………..22
10. Mean SWE ratios and confidence intervals for the SWE measurements
at the Sault Ste. Marie, MI first-order station. Note the skewed distribution of the
data, weighted to the lower ratios (mean -1 standard deviation). ……………………….22
11. Mean SWE ratios and upper confidence limit for the snow course
at Hawk Junction, ON. The lower confidence interval was omitted because the
calculations would result in a lower ratio than is found in nature (<1.5:1)……………...23
12a. Cooperative stations within the area of influence of the Duluth, MN first-order
station.……………………………………………………………………………………24
12b. Areas of influence of the first-order stations and snow courses (i.e. conversion
stations)…………………………………………………………………………………..25
12c. Total areas of influence of the first-order stations and snow courses………………26
13. Plot of regression equation used to estimate SWE ratios for snow course #49……..28
14. Flowchart illustrating the procedure used to convert the estimates of mean snow
depth from the cooperative station archives to SWE using the ratios of depth to SWE
calculated at the first-order stations and snow courses…………………………………..32
15a. Estimate of mean SWE for early March (Julian days 61-75)…………………….. 35
vi
15b. NOHRSC gamma survey estimate of SWE for March 11, 1999………………..…36
15c. Departure from normal for March 11, 1999………………………………………..37
16. SWE ratios for the NWS first-order station in St Cloud, MN (1979-1996). Note the
large number of ratios of exactly 15:1 and 10:1…………………………………...…….40
vii
LIST OF APPENDICES
Appendix A. Estimates of mean SWE.
Figure A1. Mean estimate of SWE for Julian days 1 – 15…………………………....43
Figure A2. Mean estimate of SWE for Julian days 16 – 30………………………..…44
Figure A3. Mean estimate of SWE for Julian days 31 – 45………………………..…45
Figure A4. Mean estimate of SWE for Julian days 46 – 60………………………..…46
Figure A5. Mean estimate of SWE for Julian days 61 – 75………………………..…47
Figure A6. Mean estimate of SWE for Julian days 76 – 90………………………..…48
Figure A7. Mean estimate of SWE for Julian days 91 – 105……………………....…49
Figure A8. Mean estimate of SWE for Julian days 106 – 120………………..…....…50
Figure A9. Mean estimate of SWE for Julian days 121 – 135……………..……....…51
Appendix B. Estimates of mean +1 standard deviation SWE.
Figure B1. Mean +1 standard deviation (light) estimate of Snow Water Equivalent
(SWE) for Julian days 1 – 15………………………………………………………….52
Figure B2. Mean +1 standard deviation (light) estimate of Snow Water Equivalent
(SWE) for Julian days 31 – 45…………………………………..…………..………...53
Figure B3. Mean +1 standard deviation (light) estimate of Snow Water Equivalent
(SWE) for Julian days 46 – 60. ………………………………………………..……...54
Figure B4. Mean +1 standard deviation (light) estimate of Snow Water Equivalent
(SWE) for Julian days 61 – 75. ……………………………………………..………...55
Figure B5. Mean +1 standard deviation (light) estimate of Snow Water Equivalent
(SWE) for Julian days 76 – 90. ………………………………………………..……...56
Figure B6. Mean +1 standard deviation (light) estimate of Snow Water Equivalent
(SWE) for Julian days 91 – 105. …………………………………………..…..……...57
viii
Appendix C. Estimates of mean –1 standard deviation SWE.
Figure C1. Mean -1 standard deviation (heavy) estimate of Snow Water Equivalent
(SWE) for Julian days 1 – 15. ……………….…….………………………………...58
Figure C2. Mean -1 standard deviation (heavy) estimate of Snow Water Equivalent
(SWE) for Julian days 31 – 45. …………….…….………………………………….59
Figure C3. Mean -1 standard deviation (heavy) estimate of Snow Water Equivalent
(SWE) for Julian days 46 – 60. ……………………………………………………...60
Figure C4 Mean -1 standard deviation (heavy) estimate of Snow Water Equivalent
(SWE) for Julian days 61 – 75. ……………………………………………………...61
Figure C5. Mean -1 standard deviation (heavy) estimate of Snow Water Equivalent
(SWE) for Julian days 76 – 90. ……………………………………………………...62
Figure C6. Mean -1 standard deviation (heavy) estimate of Snow Water Equivalent
(SWE) for Julian days 91 – 105. …………………………………..………………...63
ix
INTRODUCTION
Lake Superior flows east through the St. Marys River into Lake Huron at a 0.014%
gradient, dropping 6.1 m in 1.2 km. The natural outflow from Lake Superior has been managed
since the construction of the first lock in 1797. The power of the river was harnessed in 1822
when a raceway and sawmill were built by the U.S. Army Corps of Engineers (USACE). The
outflow of the river has been significantly affected by subsequent construction of locks and
hydroelectric power plants. The flow from Lake Superior has been completely regulated since
1922 with the completion of the "compensating works", which consists of a gated dam at the
head of the rapids (Figure 1). Spanning the international border, this dam provides electric
power for the United States and Canada as well as serving as a tool for regulating the levels of
Lake Superior, Lake Michigan, and Lake Huron (USACE, 1993).
The International Boundary Waters Treaty of 1909 placed the International Joint
Commission (IJC) in charge of the regulation of the outflow from Lake Superior. The Order of
Approval in 1914 required that the level of Lake Superior be maintained within a specified range
while guarding against extremely high levels downstream. Since the original Order in 1914,
seven separate plans have been instituted to regulate Lake Superior outflows (USACE, 1993).
Plan 1977-A, the present regulation plan in effect for Lake Superior, is limited by the
maximum outflow capacity of the Compensating Works on the St. Marys River. The plan also
limits the minimum and maximum monthly outflow from Lake Superior. Within these
constraints, the USACE can modify or maintain the level of Lake Superior, as well as Lakes
Huron and Michigan as needed. This plan uses a forecast of future outflow to maintain a smooth
transition of flow on a monthly basis. Since this forecast estimates outflow five months in
advance, it is also necessary to estimate input and output values of over-lake precipitation,
evaporation, and run-off from snow and rain (USACE, 1993).
1
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Sault Ste. Marie, Ontario
Compensating Works
Railway Bridge
Ca
nad
a
Un
ited
S ta
tes
International Bridge
Sault Ste. Marie, Michigan
Figure 1. Compensating Works at Sault Ste. Marie.
2
Goals of this Study
The hydrologic budget of Lake Superior is very dependent on snowfall
accumulation or depth, snow water equivalent (SWE), and the timing of the melt.
Those interested in flood forecasting, water supply, and regulation of Lake Superior
require estimates of current values of SWE and ideally would have knowledge
concerning the "normal" or mean values of SWE at various times of the snow season.
Since current SWE conditions are often reported as an average for each sub-basin, the
normals for the sub-basins would also be helpful. These mean values would enable
forecasters to make water supply and regulatory decisions with greater lead times and
accuracy based on previous operating and climate scenarios. Several agencies in the
United States and Canada have been collecting and archiving snow data, which is
used to calculate SWE normals for the Lake Superior basin.
The goals of this project are to 1) establish a framework for developing SWE
"normals" on a bi-weekly basis for the Lake Superior basin through the use of a
Geographical Information System (GIS) and historical snow data; 2) provide a
methodology to estimate historical normals or trends; and 3) provide a means of
estimating a departure from normal for all or individual sub-basins within the Lake
Superior watershed.
Data sources included: Ontario Hydro, Ontario Ministry of Natural Resources,
The National Oceanic and Atmospheric Administration (NOAA), National
Operational Hydrologic Remote Sensing Center (NOHRSC), and North Central River
Forecast Center (NCRFC). These data sources include both ground data and airborne
(gamma) survey data produced from flights over portions of the basin.
3
DATA AND STUDY AREA
Study Area
The study area encompasses the Lake Superior drainage basin, which is
approximately 211,400 km2, with Lake Superior itself being 83,400 km2 and the remaining
land drainage encompassing 128,000 km2. The U.S. Army Corps of Engineers (USACE)
recognizes 23 major sub-basins within the Lake Superior basin with the majority of the
greater basin area located in Ontario, Canada (Figure 2). At the request of the USACE, all
islands in Lake Superior were excluded from the analyses in this project. The study area for
this project includes the entire Lake Superior basin and a rectangular buffer area
approximately 60km wide and its narrowest point. The buffer area was included to allow for
interpolation of SWE across the basin boundaries using data from stations and flight lines
outside the basin. In addition, while few professionally-staffed weather stations were located
within the basin, several existed in close proximity to the basin.
The regional climate of the central and eastern portion of the basin is characterized as
maritime during ice-free periods, and progressively becomes more continental polar as lake
ice develops. Lake Superior, rather than topography, dominates the relatively flat terrain of
Michigan and Northwestern Wisconsin (210-245 meters above sea level), while the abrupt
rise in the mean elevation of Northeastern Canada (450 meters above sea level) increases the
precipitation in that region (NCDC, 1999). Mean annual snowfall in the region ranges from
315 cm at Sault St. Marie, MI on the eastern side of the lake to 447 cm at Marquette, MI in
the central Upper Peninsula (Midwestern Climate Center, 1999).
Except for those areas in close proximity to Lake Superior, the western portion of the
basin is influenced by moisture moving into the area from the Pacific and the Gulf of Mexico
(NCDC, 1999). Cold, dry winters with little precipitation are common, with mean annual
4
Ontario
Minnesota
Lake Superior
Michigan
an
ichig
eM
Lak
Wisconsin
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: July 1999 - Paul Crocker
70
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70
140
210 Kilometers
Lak
e
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Great Lakes
Rivers
Inland lakes
State/Provincial boundaries
Sub-basins
Figure 2. Study area and base coverages
5
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snowfall ranging from 114 cm at St. Cloud, MN in the southeastern region of the study area
to 155 cm at International Falls,MN near the international border. On the western shore of
Lake Superior, Duluth, MN receives an average of 198 cm of snowfall (Midwestern Climate
Center, 1999).
Thematic layers for the GIS base maps were obtained for the study area from several
sources, and it was necessary to establish a common projection and coordinate system for all
layers in the project (Table 1). Since the accurate representation of area was important, the
Albers equal area conical projection was used, with the units set to feet. The first and second
parallels were 29.30º and 45.30º north latitude, and the central meridian defined as 88.15º
west longitude. A false easting of 600,000 feet was applied to all coverages to eliminate
negative coordinates in the study area. The NAD27 datum was used along with the Clarke
1866 spheroid.
Table 1. Description of base coverages and their sources.
Coverage Name
Description
Source
superior
Lake Superior
USACE1
Gamma_f
Gamma flight lines
USACE
Gamma_c
Flight line centroids
USACE
coebasin
Basin boundaries
USACE
Sm_lakes
Hydrology
ESRI2
boundary
Study area boundary
MTU3
Ls_cnty
County lines – US
NOHRSC
Ls_state
State boundaries
NOHRSC
1
US Army Corps of Engineers
Environmental Systems Research Institute
3
Michigan Technological University
2
6
Snow data in the Lake Superior basin is sparse for portions of the basin and varies in quality.
First-order National Weather Service stations measure SWE, but have been established at
only four locations in the Lake Superior basin. A spatially denser network of cooperative
stations exists for the United States and Canada. However, they rarely measure SWE (Wilks
and McKay 1996). In Ontario, a small network of snow courses for measuring SWE and
snow depth is maintained.
Gamma Survey Flight Data - SWE
The National Operational Hydrologic Remote Sensing Center (NOHRSC), part of
NOAA's National Weather Service, is based in Chanhassen, Minnesota and operates the
Airborne Gamma Survey Program. This program provides annual measurements of SWE for
1700 flight lines in the continental United States and portions of Canada, 146 of which are in
the study area (Figure 3). The gamma flight survey data for the snow seasons of 1980 to
present is readily available from the NOHRSC on either CD-ROM or from the NOHRSC
Internet web site (NOHRSC, 1999). The data are in ASCII format and include the flight line,
flight date, SWE measurement (cm), and the latitude and longitude coordinates of the flight
line centroid. GIS vector coverages of the flight lines are available in Arc/Info format.
Sensors aboard low-flying aircraft are used to measure the gamma radiation that is
naturally emitted from isotopes occurring in the upper 20 cm of the soil. Water in the soil or
snow cover attenuates the terrestrial radiation signal, thereby providing researchers with a
tool with which to measure SWE (Carroll and Carroll, 1989). The difference between
radiation measurements made over bare ground and over snow covered ground are used to
calculate the mean SWE for a flight line. With proper calibration and corrections for
7
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: July 1999 - Paul Crocker
50
0
Gamma survey flight lines
Sub-basins
Great Lakes
Rivers
Inland lakes
State/Provincial boundaries
50 100 150 Kilometers
Figure 3. Gamma Survey flight line locations in the Lake Superior region
8
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extraneous radiation and soil moisture, gamma survey SWE estimates can often be made to
an accuracy of better than 16mm (Grasty, 1979). Kuittinen (1986) reported measurement
errors of 5-10% for similar surveys conducted in Finland.
The measurements made from the gamma surveys are integrated over the flight line
area, which is typically 16 km in length and 300m wide, covering an average of 4.8 km2.
Because of the spatial integration, the gamma flight SWE estimates account for much more
of the variability inherent in the snow pack than single point samples at ground locations and
are more representative of the current snow conditions than ground sampling (NOHRSC,
1999; Goodison et al, 1981). Ground samples tend to underestimate SWE because they
cannot fully account for the natural variability in the snow pack (Goodison et al., 1981),
while the gamma survey flights may tend towards a slight overestimation of SWE,
particularly if the background soil moisture is misrepresented. Hydrologists at the Office of
Hydrology assume a soil moisture value of 35% in their gamma calculations, which is
probably higher than the actual conditions (NOHRSC 1999).
Gamma surveys are expensive and therefore only conducted once or twice each snow
season for a given flight line (Kuittenen, 1986; NOHRSC, 1999). The flight schedules and
basins surveyed are determined less than two weeks prior to flying, usually in February and
March to aid in flood predictions (NOHRSC, 1999). In addition, some flight lines may only
be sampled once every three or four years. The lack of extensive temporal coverage
throughout the snow season limits the use of gamma survey data in historical studies.
9
NWS Cooperative Data - Snow Depth and SWE
In contrast to the gamma survey data, the NWS TD-3200 Series Cooperative data is
the most extensive data set available in terms of both time of record and spatial distribution;
many stations have been measuring snow depth since the late 1940's or earlier. The data are
collected by a network of cooperative observers and includes daily measurements of
precipitation, temperature, and snow depth. There are approximately 8,000 active
cooperative stations in the entire network, and about 23,000 stations represented in the
archives (NCDC, 1994). Roughly 200 of these stations are found in the U.S. portion of the
Lake Superior basin and these have recorded data for various time periods since 1948. The
majority of these stations are staffed by unpaid volunteers. First-order stations are operated
by highly trained observers (NCDC, 1994). First-order stations collect SWE in addition to
the measurements listed above. The spatial extent of first-order station data is quite limited
since there are only four first-order stations within the Lake Superior region, with just two
stations in the basin; all of the first-order stations in the study area are in the United States
(Figure 4).
These historical data were converted from existing digital files by the National
Climatic Data Center (NCDC) in 1982. The archived "data have received a high measure of
quality control through computer and manual edits" (NCDC, 1994). The data are stored in an
element structure in ASCII format that organizes the data in fixed-length records. Since the
archives contain filler values (e.g. -9999) to account for missing data and to maintain the
fixed-length format, it may be necessary to modify the data before analysis. The NCDC
(1994) provides some guidelines and examples of FORTRAN code for extracting and
reorganizing the data.
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Figure 4. NWS First order and cooperative stations in the Lake Superior region
11
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Snow boards and snow rulers are used to measure snowfall and cumulative snow depth at
the volunteer-run cooperative stations. Snowfall is the amount of snow deposited in a "short"
period of time, and is measured by placing a wooden or cloth-covered metal panel on the
snowpack prior to a precipitation event. The depth of accumulated snow on the panel is then
measured and recorded as snowfall. Cumulative snow depth can be measured with either a ruler
or snow tube. Measurements of snow depth taken with boards and rulers are somewhat
subjective since they are dependent on observer judgement of the average depth, and often
require numerous individual measurements to account for the variation due to drifting (Goodison
et al., 1981).
At first-order stations, snow tubes are used to sample depth and extract a snow core from
the snow pack. SWE is estimated by weighing the core with a calibrated scale. Measurements
can be subjective, but the measurement error can be reduced by a well-planned snow-course. It
is cost-prohibitive to use ground samples to obtain sufficient information to account for the
variation in the snow pack in comparison to the gamma flight surveys. However, ground
samples consistently made over several snow seasons can provide a representative index of
normal conditions (Goodison et al., 1981).
Caution must be exercised when interpreting and comparing historical climate data,
especially when using data collected at volunteer cooperative stations. Inconsistencies exist in
the data as a result of measurement errors, changes in station location, changes in observers,
different measurement methods, and the properties of the snow itself (Doesken and Judson,
1996). The effects of these inconsistencies can be subtle or profound. Doesken and Judson
(1996) stated that "winter precipitation and snowfall totals may differ by 25 percent or more
depending on station exposure and observing procedures".
12
Canadian Snow Courses and Cooperative Stations
The Ontario Ministry of Natural Resources (OMNR) and Ontario Hydro maintain snow
course data archives for the Canadian portion of the basin (Figure 5). These data include daily
SWE and depth measurements, and greatly complement the TD-3200 data series available for the
U.S. portion of the basin. Site selection for snow course sites considers the effects of terrain and
the representativeness of the snow cover. Ideally, individual snow course locations should be
permanently documented to ensure consistency of the data over time (Goodison et al., 1981).
The data are available in ASCII format and include mean monthly SWE and snow depth
values for various snow courses. Mean SWE estimates for the sub-basins in the Lake Superior
watershed are also available from these sources and the USACE - Detroit District. The Canadian
cooperative stations measure snow depth similar to the NWS cooperative stations (Figure 6). As
a result, the limitations and advantages of the Canadian data are similar to the TD-3200 data set.
Snow depth and density (SWE) is typically measured using snow tubes at the snow
courses. Measurements are taken at several points along a permanently marked transect and
averaged to produce a composite measurement that is generally representative of the area in
which the snow course is located (Goodison et al., 1981; Warren et al., 1998). Snow courses are
essentially point samples, because they represent an overall average of several point samples
along a transect and do not integrate SWE over a large area like the gamma surveys. In addition,
they have some of the same limitations as the cooperative stations, but account for more of the
natural variation in the snow pack than do the cooperative stations. The spatial and temporal
coverage of the snow course network in Ontario is similar to that of the cooperative stations and
has the same advantages over the gamma flight surveys as do the cooperative stations.
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Houghton, MI 49931-1295
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Figure 5. Canadian snow courses in the Lake Superior region
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Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: July 1999 - Paul Crocker
50
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Sub-basins
Great Lakes
Rivers
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State/Provincial boundaries
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Figure 6. Canadian cooperative stations in the Lake Superior region
15
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METHODS
Overview of Methodology
In order to take advantage of the large amount of snow depth data available in the
NWS cooperative observer network, it was decided to convert snow depth to SWE. The
cooperative observer network was the only source that provided data with a long period of
record; in addition it had the greatest spatial distribution. A review of the literature revealed
few studies for converting snow depth to SWE, particularly in the Great Lakes region.
Doesken and Judson (1996) reported a mean ratio (depth to SWE) of 13:1 for newly
fallen snow. However, it is difficult to extrapolate the results of Doesken and Judsen (1996)
to our study for several reasons. First, the ratio of 13:1 is applicable only to newly fallen
snow and not to a snow pack that is several months old and has had the opportunity to
become more dense. The use of the 13:1 ratio would result in an underestimation of the total
volume of water in the snow pack as measurements at the first-order cooperative stations
demonstrated that ratios consistently decrease throughout the snow season. Finally, the firstorder station data demonstrated that ratios vary according to geographic location, particularly
with those stations in close proximity to Lake Superior. Those stations on the lee side of
Lake Superior experience greater lake effect snowfall than stations farther inland; as the lake
effect increases, the ratios are reduced (Goodison et al. 1982).
Wilks and McKay (1996) investigated methods of estimating mean annual SWE
using the snow depth measurements made by the cooperative observer network. Their
methods were useful for estimating the annual SWE maxima for each cooperative station, but
not the bi-weekly means. While their study provided some useful insight into the statistical
distribution of the data, their methods were not directly applicable to this project.
16
Calculation of Mean SWE Values
The first-order stations and snow courses that provided both depth and SWE were
used to convert snow depth to SWE for the cooperative stations that only reported snow
depth. At each first-order station, corresponding pairs of snow depth and SWE were
retrieved and the corresponding SWE ratio was calculated. For the purposes of this study,
we term this ratio the SWE_ratio, as defined by:
SWE _ ratio s ,t 
( snow depth) s,t
[1]
SWE s ,t
where s is the station making the measurement and t is the time period of interest.
Tukey's significant difference procedure (TSD) (Mason et al. 1989) was performed
on the mean SWE ratios for the four U.S. first-order cooperative stations to determine if there
was a statistically significant difference among the ratios at different stations. Two averages
were determined to be different if:
y i  y j  TSD
[2]
where yi and y j are average SWE ratios from different stations, i and j, and

ni1  n j 1 
TSD  q( ; k , v) MS E

2


1/ 2
[3]
where (q; ) is the studentized range statistic, k is the number of averages being compared,
 is the experiment wise Type I error rate, MSE is the mean squared error from an ANOVA fit
to the data based on  degrees of freedom. This analysis provided evidence (p>0.001) that
the ratio of depth to SWE differed for each station for any given time period in the snow
season, which supports the expectations of Doesken and Judson (1996).
17
Mean SWE ratios were then calculated for each first-order station using a moving 15Julian day average. For example, at each first-order station, the long-term average snow
depth, snow water equivalent, and corresponding SWE ratios are calculated for a given 15day period. This process was completed for successive 15-Julian day periods (i.e. 1-15, 1630, 31-45, etc.). The SWE ratios were then applied to the nearby cooperative stations that
recorded only snow depth to estimate a SWE value by applying Equation 4:
SWE current station 
( snow depth) current station
( SWE ratio) nearest first -order station
[4]
The first-order stations and snow courses are hereafter referred to as conversion
stations to distinguish them from the cooperative stations and to highlight their role in the
conversion process. Since the SWE ratio at each conversion station was different, the zone
of influence about each of these stations was calculated to determine which cooperative
stations were within the zone of influence of each conversion station. The semivariance of
an arbitrary set of cooperative station depth measurements from a single time period was
used to determine the zone of influence (Figure 7), (Burrough and McDonnell 1998). This
allowed us to convert depth to SWE for each cooperative station based on the ratios unique to
that area. The range a on the semivariogram indicated that the zone of influence was within
a 165 km radius of each conversion station. The individual zones of influence for each
station overlapped to varying extents with the neighboring zones, and some regions in the
study area remained outside of any zone of influence.
18
14
12
semivariance
sill
10
C1
8
6
4
range a
2
0
0
50000
100000
150000
200000
250000
distance (m)
Figure 7. Semivariogram created in Arc/Info used to determine
the zone of influence of the conversion stations. Range a illustrates the maximum distance
of influence was 165,000 meters.
For those cooperative stations located within overlapping zones of influence, the
Euclidean distance between the cooperative station in question and the conversion stations
with the overlapping zones of influence was measured in the GIS. The cooperative station
was then assigned the bi-weekly mean SWE ratios of the conversion station. These ratios
were used to covert the depth measurements at the cooperative station to SWE.
Once the bi-weekly mean snow depth was converted to SWE for each cooperative
station, the spherical model of the kriging algorithm was used to interpolate SWE values for
the entire basin. A polygon coverage of Lake Superior was used as what ESRI Arc/Info
terms a barrier coverage. This prevented the kriging algorithm from interpolating SWE
values across the lake. The pseudo-SWE values at the cooperative stations and the directly
measured SWE values at the first-order stations and snow courses were used in the
interpolation algorithm.
19
Calculation of Confidence Intervals
The variance of the data about the mean at each station was calculated for each biweekly interval. The mean SWE ratios were not normally distributed. Therefore the skew of
the ratios was calculated for each conversion station for each bi-weekly interval (Equation 5).
n
 xj  x 
skew 


(n  1)(n  2)  s 
3
[5]
A Log Pearson Type III distribution was applied to the variances to account for the
skew in the data (mean skew = 0.91). SWE values at ± one standard deviation were
calculated for each time interval using the corrected variances. This resulted in the ability to
illustrate historical trends of SWE normals and ± one standard deviation for any point in time
during the time January 1 through April 30. This process was completed for all first-order
stations and snow courses.
20
RESULTS
An example of the historical SWE ratios calculated for a first-order station (Sault St.
Marie, MI) is illustrated in Figure 8. Note that except for the period around Julian day 20,
the lower limit tends to be well defined, while the upper limit tends to have a fuzzier
boundary. This well-defined lower limit (low SWE ratios) is essentially the upper limit, or
maximum density, that the snow pack attains. This also provides an estimate of the
maximum water equivalent in the pack.
Figure 9 illustrates the historical SWE ratios for the Hawk Junction, ON snow course.
Note that the Canadian snow course data were bi-weekly and thus demonstrated less
variation than the U.S. cooperative data. However, further analysis of the raw data resulted
in variances comparable to the NWS first-order station data. Figures 10 and 11 illustrate the
historical normal trends along with estimates at mean plus/minus one
SWE ratio (depth/SWE)
18.00
16.00
14.00
12.00
10.00
8.00
6.00
4.00
2.00
0.00
0
20
40
60
80
100
120
Julian Days
Figure 8. All SWE ratios on record for the first-order station in Sault Ste. Marie, MI
21
SWE ratios (depth/SWE)
8
7
6
5
4
3
2
1
0
0
20
40
60
80
100
120
140
Julian Days
SWE ratio (SWE/depth)
Figure 9. All SWE ratios on record for the snow course at Hawk Junction, ON. Note that
snow course measurements were only made at bi-weekly intervals
10.00
9.00
mean
8.00
7.00
6.00
+1 standard
deviation
5.00
4.00
3.00
2.00
-1 standard
deviation
Implied
deviation
1.00
0.00
1
15
30
45
60
75
90 105 120
Julian Days
Figure 10. Mean SWE ratios and confidence intervals for the SWE measurements
at the Sault Ste. Marie, MI first-order station. Note the skewed distribution of the
data, weighted to the lower ratios (mean -1 standard deviation).
22
SWE ratios (SWE/depth)
16.00
14.00
Mean
12.00
10.00
Mean +1 standard
deviation
8.00
6.00
4.00
2.00
0.00
1
15
30
45
60
75
90 105 120
Implied deviation
(no variance
provided for this
time period)
Julian Days
Figure 11. Mean SWE ratios and upper confidence limit for the snow course
at Hawk Junction, ON. The lower confidence interval was omitted because the calculations
would result in a lower ratio than is found in nature (<1.5:1).
standard deviation. The low ratios in the late spring combined with the naturally large
variation of the data resulted in unrealistically low SWE ratios for the mean minus one
standard deviation estimates; estimated ratios were often less than 1.5:1 and occasionally
resulted in a negative ratio. All of the estimates for mean minus one standard deviation were
therefore omitted for late spring (>105 Julian days).
Figure 12a illustrates the area of influence of the Duluth, MN station, while Figures
12b and 12c illustrate the area of influence of all first-order stations and snow courses. The
cooperative stations that fell within the area of influence of each station were assigned the
corresponding conversion ratio for each 15-day period. In this manner, we were able to
account for the spatial and temporal variation in SWE for the period of record of the
cooperative observer network.
23
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Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: July 1999 - Paul Crocker
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Figure 12a. Cooperative stations within the area of influence of the Duluth, MN first order station.
24
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Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: July 1999 - Paul Crocker
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Figure 12b. Areas of influence of the first order stations and snow courses (IE conversion stations)
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School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: July 1999 - Paul Crocker
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Figure 12c. Areas of influence of the first order stations and snow courses (IE conversion stations)
26
Most of the cooperative stations in the basin were within the area of influence of a
first-order station or snow course; however, portions of the western and central Upper
Peninsula of Michigan were not within the area of influence of a first-order station (Figure
12c). Knowledge of the local climate and snowfall tendencies was used to determine the
first-order station that was most similar to the area in western and central Upper Michigan
not represented by a first-order station. The conversion ratios from the Sault Saint Marie, MI
station were applied to the stations in this area to fill in the lack of coverage in the data.
Overlapping areas of influence were resolved by assigning cooperative stations to the nearest
conversion station. The GIS was used to interpolate SWE values for the entire basin in a
raster coverage using the SWE estimates from the first-order stations, snow courses, and
pseudo-SWE values at the cooperative stations as input.
Some Canadian snow courses did not provide mean snow depths or SWE for all of
the 15-day periods due to incomplete data. The time periods covering late January and late
February were greatly affected by this lack of data (Table 2). A snow course was deemed to
have a sufficient period of record if there were snow depth and SWE measurements for more
than ten years. Linear regression was utilized to estimate values for those time periods with
missing data (Figure 13).
27
Table 2. Bi-weekly mean SWE ratios (depth/SWE) for the Canadian snow courses. Values
in bold are estimated using linear regression.
Julian Date
30
45
1
15
Survey
Dog Lake Dam (#42)
60
75
90
105
120
5.42
5.42
5.43
4.91
4.79
4.34
3.85
3.29
3.56
Armstrong (#49)
5.63
5.68
5.48
5.11
5.03
4.96
4.35
3.72
3.46
Cameron Falls (#56)
5.67
5.77
5.71
5.17
5.16
4.77
4.31
3.74
3.55
Long Lake Dam (#63)
5.76
5.54
5.20
4.89
4.67
4.29
3.97
3.56
3.11
Geraldton (#70)
6.28
6.07
5.59
5.40
5.24
4.95
4.54
3.98
3.46
Wig Lake (#77)
6.82
6.33
5.64
5.61
5.26
5.02
4.65
4.16
3.71
White River (#84)
5.24
5.33
5.37
4.77
4.68
4.22
3.99
3.66
3.19
Hawk Junction (#98)
5.38
5.06
4.63
4.36
4.08
3.67
3.42
2.97
2.53
SWE ratio (depth/SWE)
6.00
5.50
5.00
4.50
4.00
2
y = -0.0002x + 0.0011x + 5.6209
2
R = 0.9799
3.50
3.00
0
20
40
60
80
100
120
140
Julian Days
Figure 13. Linear regression equation used to estimate SWE ratios for snow course #49.
Note missing data points for Julian days 15 and 45.
28
The accuracy of the interpolation was tested by calculating the residuals of the
interpolation and testing to see if they differed from zero. For each biweekly period, the
pseudo-SWE values at each cooperative were subtracted from the SWE values in the final
interpolation. A Student's t-test (Equation 5) verified that the predicted values of the
interpolation did not differ from the actual values (p>0.001)(Mason et al. 1989).
t
n1 / 2 ( y   )
s
[6]
Comparison to Gamma Flight Data
In an operational mode, the USACE compares the estimated SWE normals with
current conditions in the Lake Superior basin. In particular, the airborne gamma surveys are
heavily relied upon for current conditions during the spring melt period. A comparison
between the SWE values in the cooperative network to an estimated value of SWE from a
gamma flight was made; the cooperative station values included depth measurements
converted to SWE using the SWE ratios. All cooperative observer stations within 8 km (5
miles) of gamma flight centroids were located using the GIS.
Corresponding pairs of SWE estimates from the gamma flight and the cooperative
observer network were compared. There were relatively few pairs of data that corresponded
in both time and space; those that existed are illustrated in Table 3. Goodison et al (1981)
reported that the gamma surveys yield higher SWE estimates that the cooperative network
because of the high soil moisture value (35%) used by hydrologists in the gamma flight
calculations. The comparisons in Table 3 do not reflect this expectation. It is difficult to
make any assumptions based on five samples, but these results indicate that an investigation
29
should be made determine if the gamma surveys in the Lake Superior basin actually
overestimate SWE. If portions of the soil remained unfrozen under the snowpack, it is
possible that continuous melt at the bottom of the snowpack could result in a higher moisture
content than would be found in the soils of the prairies, where some of these assumptions
were made.
Table 3. Comparison of cooperative station estimates with gamma survey estimates (all
values in cm of water)
Gamma Flight #
Gamma SWE
Cooperative Station
Cooperative
Estimate
#
Station SWE
Estimate
LS382
19.8
203908
13.0
LS395
13.2
207190
8.6
LS379
10.9
203744
15.3
LS333
7.1
212645
7.1
LS163
5.1
475286
12.4
GIS & Applications
Arc/Info v.7.1.1 on a Unix Workstation, ArcView v.3.0 on Unix, and ArcView v.3.1
on Windows NT were used for the GIS analysis. MS Excel 5.0, MS Excel 97, and MS
Access 97 were used to manipulate the archived snowpack data and conduct simple statistical
analysis prior to the GIS analyses. SAS v.6.12 was used for advanced statistical analyses.
Coordinates for the cooperative stations, first-order stations, gamma flight centroids,
and snow courses were used to create point coverages of the snowpack data. Snowpack data
values were derived from the data archives using the methods described above, with the final
30
attributes being written to text files. These text files were imported into Arc/Info to create
the point-attribute-tables (.PAT) for the point coverages.
A box was drawn to enclose an area that included a buffer of roughly 40 miles about
the basin. This box, saved as a polygon in vector format, was then used as a clip template for
the boundary of the study area for all thematic layers used and created in the project.
The kriging function in Arc/Info was used to interpolate values for the entire basin
from the point coverages for all SWE estimates. The sampling density for the kriging was
arbitrarily set at 250 points across the x axis, which resulted in a spatial resolution of slightly
over 3km (~10,000 feet) for the output surface grids. The polygon coverage of Lake Superior
was used as a barrier coverage to prevent the algorithm from interpolating SWE values
across Lake Superior. Appendices A through C illustrate the coverages of estimated SWE
coverage derived from this study for normal and plus/minus one standard deviation.
The mean SWE for each of the individual sub-basins was calculated using the
ZONALMEAN command in Arc/Info. The results of these calculations were converted to
INFO tables and attached to the attribute table of the sub-basin Arc/Info polygon coverage.
Figures 14 illustrates the GIS methods as a flowchart.
31
Coop station
point coverage
Calculate
semivariance in
Arcinfo
Depth values
at coop
stations
First-order
stations and
snow courses
Sort data in
DBMS by
Julian date
semivariogram
Sort data in
DBMS by
Julian date
Determine
zone of
influence of
each station
Distribute firstorder stations and
snow courses to
coop stations
according to
zones of
influence
SWE and depth
values
Depth/SWE = ratio
Sorted depth
values
Apply SWE
ratios
Converted
SWE
values
SWE
ratios
Figure 14. Flowchart illustrating the procedure used to convert the estimates of mean snow depth from the cooperative station
archives to SWE using the ratios of depth to SWE calculated at the first-order stations and snow courses.
32
Data Products
The original proposal for this project called for the delivery of several data products.
In addition to several base coverages to be used for map creation, bi-weekly estimates of
SWE for both the entire Lake Superior basin and for its primary sub-basins were created. All
NOHRSC Gamma Survey archives were converted to spatial coverages and database (INFO)
files. Database files were compiled for the NOAA and Ontario climate data that were used to
create the estimates. The database was provided to the USACE, Detroit District as part of the
project.
Base Coverages
Several sources were used to create base coverages that were used to generate maps
of the raw SWE data and SWE estimates. These included hydrology, political boundaries,
sub-basin boundaries, and point coverages illustrating the locations of the gamma surveys,
snow courses, and cooperative stations.
Bi-weekly SWE Estimates
Several project files were created in ESRI Arcview for the display and hardcopy
output of the SWE estimate grids. These include the mean and ± 1 standard deviation SWE
estimates, with SWE calculated in both metric and English units. There was insufficient data
to calculate the variance of the SWE measurements for the periods of Julian days 16-30, 106120, and 121-135. Subsequently, no light or heavy estimates were created for those time
periods. The mean SWE estimates for the sub-basins are included in the polygon attribute
table (.pat) of the basins coverage.
33
Gamma Survey Flights
The archives of the Gamma flights were converted to INFO tables and were
subsequently referenced to the Gamma flight (gamma_flt) arc coverage using a relate in
ArcView. The flight line name and number (eg LS121) were used as the relate field. These
data can be sorted, queried, and displayed according to date, SWE values, or flight line.
Departures from Normal
For future estimates, the departure from normal can be calculated for current
conditions using the NOHRSC gamma survey results and the mean SWE estimates created in
this project. Since most of the gamma surveys are conducted in early March, the estimates of
departures from normal can usually be determined only for that time period (Julian days 61 75).
The gamma survey results are available each spring in raster format on the NOHRSC
web site. Once downloaded, the gamma survey results must be projected to the same
projection parameters as the SWE estimate grids from this project. Finally, the gamma
survey grid is subtracted from the SWE estimate grid to create a grid describing the current
departure from normal. Figures 15a - 15c illustrate this procedure in use.
34
Sub-basins
State/Provincial Boudaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Woood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: October 1999 - Paul Crocker
50
0
50
100 150
200 250 Kilometers
Figure 15a. Mean SWE estimate for Julian days 61-75.
35
Sub-basins
State/Provincial Boudaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Woood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: October 1999 - Paul Crocker
50
0
50
100 150
200 250 Kilometers
Figure 15b. NOHRSC Gamma survey estimate of SWE estimate for March 11, 1999.
36
Sub-basins
State/Provincial Boudaries
Departure from normal (cm)
> +25
+20 to +25
+15 to +20
+10 to +15
+5 to +10
0 to +5
-5 to 0
-10 to -5
-10 to -15
-15 to -20
-20 to -25
< -25
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Woood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: October 1999 - Paul Crocker
50
0
50
100 150
200 250 Kilometers
Figure 15c. Estimated departure from normal for March 11, 1999.
37
DISCUSSION
Numerous sources of snow pack data were utilized in this project. Some sources
were more appropriate for estimating SWE than the others. Table 4 illustrates the limitations
and strengths of each type of data. The individual ratios used to calculate the mean ratio for
each time period were highly variable (Figures 8 and 9) and were skewed to the lower ratios
(higher volumes water per unit of depth) in the snow pack.
Table 4. Description of the advantages and limitations of each data source in estimating
mean SWE for bi-weekly time intervals.
Source
Advantages
Limitations
Gamma Flight Survey
Highly accurate and
Sparse temporal coverage
accounts for most of the
with most measurements in
spatial variation
early March only
Cooperative station data
Good spatial and temporal
coverage
No direct measurement of
SWE and inconsistencies
may exist in the data
First-order Stations
Good temporal coverage
with accurate SWE
measurements
Very few first-order stations
exist within the basin
Canadian Snow
Courses/Cooperative
Stations
Good temporal and spatial
coverage and includes SWE
measurements
Inconsistencies may exist in
the cooperative station data
While our methods appear to be appropriate for establishing a framework for
estimating SWE normals, caution must be exercised when interpreting and comparing
historical climate data. This is especially true when using data collected at volunteer
cooperative stations. Inconsistencies exist in the data as a result of measurement errors,
changes in station location, changes in observers at a station, different measurement methods
between stations, and the properties of the snow itself (Doesken and Judson, 1996).
38
The inherent variation in the data itself, especially when expressed as a ratio of depth
to SWE, made it difficult to estimate the mean SWE with a narrow confidence interval. The
SWE ratios were most variable in the early winter (Figure 8) and were extremely variable
between October and January 1. The USACE was most interested in the SWE normals
during the melt season, so the large year-to-year and within-season variation in early winter
SWE ratios was not considered to be a problem.
The interpolations were checked visually and by calculating the residuals. While
many errors were detected and corrected using this procedure, it is inevitable that
measurement errors made at the cooperative stations were undetected by our procedures. It
should also be noted that the some data from the first-order stations exhibited a peculiar
preponderance of SWE ratios of exactly 5:1, 10:1, and 15:1 (Figure 16). These suspect ratios
may be the result of estimates being made at the first-order station of SWE based upon snow
depth measurements rather than directly measuring SWE or vice versa. Another explanation
may result from the mathematics involved in calculating the ratios. The effects of ratio
calculations and rounding errors can produce interesting phenomena similar to the
peculiarities seen here. Since some of these values may be the result of genuine
measurements, it is impractical, if not impossible, to screen for estimated SWE values in the
first-order station data. Consequently, these values were not removed from the data.
Another source of error could be attributed to the interpolations used to estimate SWE
from the pseudo-SWE estimates calculated for the cooperative stations. Radial "banding"
occurred in regions where there was a low density of sample points (i.e. cooperative stations
or snow courses). This effect was an artifact of the kriging process, and there was no viable
solution to correct for this problem. The sparse distribution of
39
20.0
SWE ratios (depth/SWE)
18.0
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
0
20
40
60
80
100
120
140
Julian Days
Figure 16. SWE ratios for the NWS first-order station in St Cloud, MN (1979-1996). Note
the large number of ratios of exactly 15:1 and 10:1.
points in the northeastern and northwestern portions of the study area also created some
peaks and depressions in the SWE estimates. The mean estimate for the time period of Julian
days 121-135 illustrates the results of insufficient point samples in the northern portion of the
study area (Appendix A9).
Figures 8 and 16 illustrate ratios lower than 2:1. It is not realistic to expect ratios
lower than this in nature, but there are some extremely low ratios evident in the data. This
could be an artifact of the measurement process. It can prove difficult to obtain an intact
snow core from the granular snow found in a melting snowpack, and the loss of snow from
the core could result in unusual estimates of SWE. Very shallow snowpacks can also make it
difficult to measure depth accurately. Rounding errors in the measurements could also be
responsible for these low ratios.
40
CONCLUSIONS AND RECOMMENDATIONS
Although there is a sparse record of quality snow pack data that accounts for most of
the natural variation in the snowpack, this project provides reasonable estimates of SWE for
the Lake Superior basin. Cooperative station data should not be used to absolutely quantify
SWE, but it is appropriate for calculating an index of SWE (Doesken and Judson, 1996).
Our methods take advantage of the dense network of cooperative stations and the known
relationships between SD and SWE at the regional first-order stations and snow courses.
The GIS coverages of the SWE estimates can be used in conjunction with the Gamma
Flight Survey data from the NOHRSC to determine the current SWE conditions. Departures
from normal can be estimated by subtracting the data coverage of the current SWE
conditions (i.e. from gamma surveys) from the mean SWE conditions estimated in this
project. It may be necessary to resample the grid size of one of the input grids to ensure
precise subtraction of the grid cells, but this is easily accomplished and would not hinder the
procedure.
Future research should investigate the potential for utilizing the gamma flight data to
adjust for variation in the cooperative station data. Again, a reasonably long period of record
would be required to use the gamma survey data as a calibration tool, but it may not be
necessary to have survey data for each bi-weekly interval to improve the pseudo-SWE
values.
There is obviously a lack of SWE measurements in the central and western Upper
Peninsula of Michigan (Fig 10c). It is strongly recommended that one or two first-order
stations be established in that region to provide a record of SWE and allow future researchers
to refine the SWE ratios for that region.
41
REFERENCES
Burrough, P. A. and R. A. McDonnell. 1998. Principals of Geographical Information
Systems. Oxford University Press.
Carroll, S. S. and T. R. Carroll. 1989. Effect of uneven snow cover on airborne snow water
equivalent estimates obtained by measuring terrestrial gamma radiation. Water Resources
Research, 25:7, 1505-1510.
Doesken, N. J. and A. Judson. 1996. The snow booklet: a guide to the science, climatology,
and measurement of snow in the United States. Colorado Climate Center, Department of
Atmospheric Science.
Goodison, B.E., H.L. Ferguson, and G.A. McKay. 1981. Measurement and Data Analysis.
Handbook of Snow.
Grasty, R.L. 23-27 April, 1979. One flight snow-water equivalent measurement by airborne
gamma-ray spectrometry. Paper presented at WMO Workshop on Remote Sensing of
Snow and Soil Moisture by Nuclear Techniques, Voss, Norway.
Kuittinen, R. 1986. Determination of aerial snow-water equivalent values using satellite
imagery and aircraft gamma-ray spectrometry. Hydrologic Applications of Space
Technology, 160.
Mason, R. L., R. F. Gunst, and J. L. Hess. 1989. Statistical Design and Analysis of
Experiments. John Wiley and Sons.
Midwestern Climate Center. 1999. Website: http://mcc.sws.uiuc.edu/
NCDC. 1994. Surface Land Daily Cooperative Summary of the Day, TD-3200. (User
documentation for the TD-3200 Series data), NCDC, Federal Building, Asheville, North
Carolina.
NCDC. 1999. Website: http://www4.ncdc.noaa.gov
NOHRSC. 1999. Airborne Gamma Survey Program. Website:
http://www.nohrsc.nws.gov/98/html/gamma/gammapage.html
USACE, North Central Division. December 1, 1993. Great Lakes Levels. Update Letter
No. 101
Wilks, D. S. and M. McKay. 1996. Extreme-value statistics for snowpack water equivalent
in the northeastern United States using the cooperative observer network. Journal of
Applied Meteorology, 35, 706-713.
42
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A1. Mean Snow Water Equivalent (SWE) estimate for Julian days 1 - 15.
43
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A2. Mean Snow Water Equivalent (SWE) estimate for Julian days 16 - 30.
44
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A3. Mean Snow Water Equivalent (SWE) estimate for Julian days 31 - 45.
45
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A4. Mean Snow Water Equivalent (SWE) estimate for Julian days 46 - 60.
46
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A5. Mean Snow Water Equivalent (SWE) estimate for Julian days 61 - 75.
47
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A6. Mean Snow Water Equivalent (SWE) estimate for Julian days 76 - 90.
48
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A7. Mean Snow Water Equivalent (SWE) estimate for Julian days 91 - 105.
49
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A8. Mean Snow Water Equivalent (SWE) estimate for Julian days 106 - 120.
50
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure A9. Mean Snow Water Equivalent (SWE) estimate for Julian days 121 - 135. Note that a complete
interpolation was not possible due to sparse sample points in the northern portion of the basin for this bi-weekly period.
51
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure B1. Light (Mean + 1 standard deviation) Snow Water Equivalent (SWE) estimate for Julian days 1 - 15.
52
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure B2. Light (Mean + 1 standard deviation) Snow Water Equivalent (SWE) estimate for Julian days 31 - 45.
53
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure B3. Light (Mean + 1 standard deviation) Snow Water Equivalent (SWE) estimate for Julian days 46 - 60.
54
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure B4. Light (Mean + 1 standard deviation) Snow Water Equivalent (SWE) estimate for Julian days 61 - 75.
55
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure B5. Light (Mean + 1 standard deviation) Snow Water Equivalent (SWE) estimate for Julian days 76 - 90.
56
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
N
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
0
50
100
150
200
250 Kilometers
Figure B6. Light (Mean + 1 standard deviation) Snow Water Equivalent (SWE) estimate for Julian days 91 - 105.
57
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
N
0
50
100
150
200
250 Kilometers
Figure C1. Heavy (Mean - 1 standard deviation) estimate of Snow Water Equivalent (SWE) for Julian days 1 - 15.
58
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
N
0
50
100
150
200
250 Kilometers
Figure C2. Heavy (Mean - 1 standard deviation) estimate of Snow Water Equivalent (SWE) for Julian days 31 - 45.
59
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
N
0
50
100
150
200
250 Kilometers
Figure C3. Heavy (Mean - 1 standard deviation) Snow Water Equivalent (SWE) estimate for Julian days 46 - 60.
60
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
N
0
50
100
150
200
250 Kilometers
Figure C4. Heavy (Mean - 1 standard deviation) estimate of Snow Water Equivalent (SWE) for Julian days 61 - 75.
61
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
N
0
50
100
150
200
250 Kilometers
Figure C5. Heavy (Mean - 1 standard deviation) estimate of Snow Water Equivalent (SWE) for Julian days 76 - 90.
62
Lakes
Sub-basins
State/Province Boundaries
SWE (cm)
> 22
20 - 22
18 - 20
16 - 18
14 - 16
12 - 14
10 - 12
8 - 10
6-8
4-6
2-4
0-2
No Data
Ecological Monitoring and Mapping Laboratory
School of Forestry and Wood Products
Michigan Technological University
Houghton, MI 49931-1295
Map Date: September 1999 - Paul Crocker
N
0
50
100
150
200
250 Kilometers
Figure C6. Heavy (Mean - 1 standard deviation) estimate of Snow Water Equivalent (SWE) for Julian days 91 - 105.
63